@article{FedchenkoTarkhanov2015,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Class of Toeplitz Operators in Several Variables},
  series = {Advances in applied Clifford algebras},
  volume    = {25},
  journal   = {Advances in applied Clifford algebras},
  number    = {4},
  publisher = {Springer},
  address   = {Basel},
  issn      = {0188-7009},
  doi       = {10.1007/s00006-015-0546-9},
  pages     = {811 -- 828},
  year      = {2015},
  abstract  = {We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory.},
  language  = {en}
}
@book{GauthierTarkhanov2004,
  author    = {Gauthier, P. M. and Tarkhanov, Nikolai Nikolaevich},
  title     = {A covering proberty of the Riemann zeta-funktion},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {11 S.},
  year      = {2004},
  language  = {en}
}
@book{Tarkhanov2003,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {A fixed point formula in one complex variable},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {14 S.},
  year      = {2003},
  language  = {en}
}
@article{FedosovSchulzeTarkhanov2001,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A general index formula on toric manifolds with conical point},
  year      = {2001},
  language  = {en}
}
@article{AlsaedyTarkhanov2017,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Hilbert Boundary Value Problem for Generalised Cauchy-Riemann Equations},
  series = {Advances in applied Clifford algebras},
  volume    = {27},
  journal   = {Advances in applied Clifford algebras},
  publisher = {Springer},
  address   = {Basel},
  issn      = {0188-7009},
  doi       = {10.1007/s00006-016-0676-8},
  pages     = {931 -- 953},
  year      = {2017},
  abstract  = {We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed problems, and construct an explicit formula for approximate solutions.},
  language  = {en}
}
@article{MakhmudovMakhmudovTarkhanov2017,
  author    = {Makhmudov, K. O. and Makhmudov, O. I. and Tarkhanov, Nikolai Nikolaevich},
  title     = {A nonstandard Cauchy problem for the heat equation},
  series = {Mathematical Notes},
  volume    = {102},
  journal   = {Mathematical Notes},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {0001-4346},
  doi       = {10.1134/S0001434617070264},
  pages     = {250 -- 260},
  year      = {2017},
  abstract  = {We consider the Cauchy problem for the heat equation in a cylinder C (T) = X x (0, T) over a domain X in R (n) , with data on a strip lying on the lateral surface. The strip is of the form S x (0, T), where S is an open subset of the boundary of X. The problem is ill-posed. Under natural restrictions on the configuration of S, we derive an explicit formula for solutions of this problem.},
  language  = {en}
}
@article{LyTarkhanov2016,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Rado theorem for p-harmonic functions},
  series = {Boletin de la Sociedad Matem{\~A}!'tica Mexicana},
  volume    = {22},
  journal   = {Boletin de la Sociedad Matem{\~A}!'tica Mexicana},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1405-213X},
  doi       = {10.1007/s40590-016-0109-7},
  pages     = {461 -- 472},
  year      = {2016},
  abstract  = {Let A be a nonlinear differential operator on an open set X subset of R-n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A(u) = 0 in XS of class F satisfies this equation weakly in all of X. For the most extensively studied classes F, we show conditions on S which guarantee that S is removable for F relative to A.},
  language  = {en}
}
@article{FedchenkoTarkhanov2017,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Rado theorem for the porous medium equation},
  series = {Boletin de la Sociedad Matem{\´a}tica Mexicana},
  volume    = {24},
  journal   = {Boletin de la Sociedad Matem{\´a}tica Mexicana},
  number    = {2},
  publisher = {Springer},
  address   = {Cham},
  issn      = {1405-213X},
  doi       = {10.1007/s40590-017-0169-3},
  pages     = {427 -- 437},
  year      = {2017},
  abstract  = {We prove that if u is a locally Lipschitz continuous function on an open set chi subset of Rn + 1 satisfying the nonlinear heat equation partial derivative(t)u = Delta(vertical bar u vertical bar(p-1) u), p > 1, weakly away from the zero set u(-1) (0) in chi, then u is a weak solution to this equation in all of chi.},
  language  = {en}
}
@article{LyTarkhanov2009,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {A variational approach to the Cauchy problem for nonlinear elliptic differential equations},
  issn      = {0928-0219},
  doi       = {10.1515/Jiip.2009.037},
  year      = {2009},
  abstract  = {We discuss the relaxation of a class of nonlinear elliptic Cauchy problems with data on a piece S of the boundary surface by means of a variational approach known in the optimal control literature as "equation error method". By the Cauchy problem is meant any boundary value problem for an unknown function y in a domain X with the property that the data on S, if combined with the differential equations in X, allow one to determine all derivatives of y on S by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near S is guaranteed by the Cauchy-Kovalevskaya theorem. We also admit overdetermined elliptic systems, in which case the set of those Cauchy data on S for which the Cauchy problem is solvable is very "thin". For this reason we discuss a variational setting of the Cauchy problem which always possesses a generalised solution.},
  language  = {en}
}
@book{KytmanovMyslivetsTarkhanov2001,
  author    = {Kytmanov, Alexander M. and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {An Asymptotic expansion of the Bochner-Martinelli integral},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgrupe Partielle Differentialgleichun},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgrupe Partielle Differentialgleichun},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-339X},
  pages     = {13 S.},
  year      = {2001},
  language  = {en}
}
@article{FedchenkoTarkhanov2015,
  author    = {Fedchenko, Dmitri and Tarkhanov, Nikolai Nikolaevich},
  title     = {An index formula for Toeplitz operators},
  series = {Complex variables and elliptic equations},
  volume    = {60},
  journal   = {Complex variables and elliptic equations},
  number    = {12},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1747-6933},
  doi       = {10.1080/17476933.2015.1050007},
  pages     = {1764 -- 1787},
  year      = {2015},
  abstract  = {We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first-order partial differential equations in a bounded domain in R-n with smooth boundary.},
  language  = {en}
}
@article{ElinShoikhetTarkhanov2017,
  author    = {Elin, Mark and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich},
  title     = {Analytic Semigroups of Holomorphic Mappings and Composition Operators},
  series = {Computational Methods and Function Theory},
  volume    = {18},
  journal   = {Computational Methods and Function Theory},
  number    = {2},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1617-9447},
  doi       = {10.1007/s40315-017-0227-x},
  pages     = {269 -- 294},
  year      = {2017},
  abstract  = {In this manuscript we provide a review on the classical and resent results related to the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators.},
  language  = {en}
}
@book{Tarkhanov2002,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Anisotropic edge problems},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {43 S.},
  year      = {2002},
  language  = {en}
}
@article{AntonioukKiselevTarkhanov2015,
  author    = {Antoniouk, Alexandra Viktorivna and Kiselev, Oleg M. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Asymptotic Solutions of the Dirichlet Problem for the Heat Equation at a Characteristic Point},
  series = {Ukrainian mathematical journal},
  volume    = {66},
  journal   = {Ukrainian mathematical journal},
  number    = {10},
  publisher = {Springer},
  address   = {New York},
  issn      = {0041-5995},
  doi       = {10.1007/s11253-015-1038-8},
  pages     = {1455 -- 1474},
  year      = {2015},
  abstract  = {The Dirichlet problem for the heat equation in a bounded domain aS, a"e (n+1) is characteristic because there are boundary points at which the boundary touches a characteristic hyperplane t = c, where c is a constant. For the first time, necessary and sufficient conditions on the boundary guaranteeing that the solution is continuous up to the characteristic point were established by Petrovskii (1934) under the assumption that the Dirichlet data are continuous. The appearance of Petrovskii's paper was stimulated by the existing interest to the investigation of general boundary-value problems for parabolic equations in bounded domains. We contribute to the study of this problem by finding a formal solution of the Dirichlet problem for the heat equation in a neighborhood of a cuspidal characteristic boundary point and analyzing its asymptotic behavior.},
  language  = {en}
}
@article{GlebovKiselevTarkhanov2010,
  author    = {Glebov, Sergei and Kiselev, Oleg and Tarkhanov, Nikolai Nikolaevich},
  title     = {Autoresonance in a dissipative system},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8113/43/21/215203},
  year      = {2010},
  abstract  = {We study the autoresonant solution of Duffing's equation in the presence of dissipation. This solution is proved to be an attracting set. We evaluate the maximal amplitude of the autoresonant solution and the time of transition from autoresonant growth of the amplitude to the mode of fast oscillations. Analytical results are illustrated by numerical simulations.},
  language  = {en}
}
@article{RabinovichSchulzeTarkhanov2004,
  author    = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Boundary value problems in oscillating cuspidal wedges},
  issn      = {0035-7596},
  year      = {2004},
  abstract  = {The paper is devoted to pseudodifferential boundary value problems in domains with cuspidal wedges. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to edges},
  language  = {en}
}
@article{Tarkhanov2008,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Cancellation of a Publication},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {2 S.},
  year      = {2008},
  language  = {en}
}
@article{Tarkhanov2016,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Deformation quantization and boundary value problems},
  series = {International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis \& topology},
  volume    = {13},
  journal   = {International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis \& topology},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0219-8878},
  doi       = {10.1142/S0219887816500079},
  pages     = {176 -- 195},
  year      = {2016},
  abstract  = {We describe a natural construction of deformation quantization on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.},
  language  = {en}
}
@article{BagderinaTarkhanov2014,
  author    = {Bagderina, Yulia Yu. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Differential invariants of a class of Lagrangian systems with two degrees of freedom},
  series = {Journal of mathematical analysis and applications},
  volume    = {410},
  journal   = {Journal of mathematical analysis and applications},
  number    = {2},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-247X},
  doi       = {10.1016/j.jmaa.2013.08.015},
  pages     = {733 -- 749},
  year      = {2014},
  language  = {en}
}
@book{ShlapunovTarkhanov2001,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Duality by reproducing kernels},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {78 S.},
  year      = {2001},
  language  = {en}
}
@article{KytmanovMyslivetsSchulzeetal.2005,
  author    = {Kytmanov, Alexander M. and Myslivets, Simona and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Elliptic problems for the Dolbeault complex},
  issn      = {0025-584X},
  year      = {2005},
  abstract  = {The inhomogeneous partial derivative-equation is an inexhaustible source of locally unsolvable equations, subelliptic estimates and other phenomena in partial differential equations. Loosely speaking, for the analysis on complex manifolds with boundary nonelliptic problems are typical rather than elliptic ones. Using explicit integral representations we assign a Fredholm complex to the Dolbeault complex over an arbitrary bounded domain in C-n. (C) 2005 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim},
  language  = {en}
}
@book{KrupchykTarkhanovTuomela2006,
  author    = {Krupchyk, K. and Tarkhanov, Nikolai Nikolaevich and Tuomela, J.},
  title     = {Elliptic quasicomplexes in boutet de monvel algebra},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {24 S.},
  year      = {2006},
  language  = {en}
}
@article{MakhmudoMakhmudovTarkhanov2011,
  author    = {Makhmudo, K. O. and Makhmudov, O. I. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Equations of Maxwell type},
  series = {Journal of mathematical analysis and applications},
  volume    = {378},
  journal   = {Journal of mathematical analysis and applications},
  number    = {1},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-247X},
  doi       = {10.1016/j.jmaa.2011.01.012},
  pages     = {64 -- 75},
  year      = {2011},
  abstract  = {For an elliptic complex of first order differential operators on a smooth manifold X, we define a system of two equations which can be thought of as abstract Maxwell equations. The formal theory of this system proves to be very similar to that of classical Maxwell's equations. The paper focuses on boundary value problems for the abstract Maxwell equations, especially on the Cauchy problem.},
  language  = {en}
}
@book{Tarkhanov2006,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Euler characteristic of Fredholm quasicomplexes},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {8 S.},
  year      = {2006},
  language  = {en}
}
@article{Tarkhanov2004,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Fixed point formula for holomorphic functions},
  issn      = {0002-9939},
  year      = {2004},
  abstract  = {We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain D with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of D, we make use of the Bergman kernel of this domain. The Lefschetz number is proved to be the sum of the usual contributions of fixed points of the map in D and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points},
  language  = {en}
}
@article{GlebovKiselevTarkhanov2011,
  author    = {Glebov, Sergei and Kiselev, Oleg and Tarkhanov, Nikolai Nikolaevich},
  title     = {Forced nonlinear resonance in a system of coupled oscillators},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {21},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {2},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.3578047},
  pages     = {7},
  year      = {2011},
  abstract  = {We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time t similar to s(-2) one component of the system is described for the most part by the inhomogeneous Mathieu equation while the other component represents pulsation of large amplitude. A Hamiltonian system is obtained which describes for the most part the behavior of the envelope in a special case. The analytic results agree with numerical simulations.},
  language  = {en}
}
@article{ShlapunovTarkhanov2007,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Formal poincare lemma},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {36 S.},
  year      = {2007},
  language  = {en}
}
@book{KrupchykTarkhanovTuomela2005,
  author    = {Krupchyk, K. and Tarkhanov, Nikolai Nikolaevich and Tuomela, J.},
  title     = {Generalised elliptic boundary problems},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {27 S.},
  year      = {2005},
  language  = {en}
}
@article{LyTarkhanov2015,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {Generalized Beltrami equations},
  series = {Complex variables and elliptic equations},
  volume    = {60},
  journal   = {Complex variables and elliptic equations},
  number    = {1},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1747-6933},
  doi       = {10.1080/17476933.2013.876759},
  pages     = {24 -- 37},
  year      = {2015},
  abstract  = {We enlarge the class of Beltrami equations by developing a stability theory for the sheaf of solutions of an overdetermined elliptic system of first-order homogeneous partial differential equations with constant coefficients in Rn.},
  language  = {en}
}
@misc{ShlapunovTarkhanov2017,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Golusin-Krylov formulas in complex analysis},
  series = {Complex variables and elliptic equations},
  volume    = {63},
  journal   = {Complex variables and elliptic equations},
  number    = {7-8},
  publisher = {Routledge},
  address   = {Abingdon},
  issn      = {1747-6933},
  doi       = {10.1080/17476933.2017.1395872},
  pages     = {1142 -- 1167},
  year      = {2017},
  abstract  = {This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces.},
  language  = {en}
}
@book{Tarkhanov2004,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Harmonic integrals on domains with edges},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {41 S.},
  year      = {2004},
  language  = {en}
}
@article{KytmanovMyslivetsTarkhanov2004,
  author    = {Kytmanov, Alexander M. and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {Holomorphic Lefschetz formula for manifolds with boundary},
  issn      = {0025-5874},
  year      = {2004},
  abstract  = {The classical Lefschetz fixed point formula expresses the number of fixed points of a continuous map f : M-->M in terms of the transformation induced by f on the cohomology of M. In 1966 Atiyah and Bott extended this formula to elliptic complexes over a compact closed manifold. In particular, they presented a holomorphic Lefschetz formula for compact complex manifolds without boundary, a result, in the framework of algebraic geometry due to Eichler (1957) for holomorphic curves. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, hence the Atiyah- Bott theory is no longer applicable. To get rid of the difficulties related to the boundary behaviour of the Dolbeault cohomology, Donelli and Fefferman (1986) derived a fixed point formula for the Bergman metric. The purpose of this paper is to present a holomorphic Lefschetz formula on a strictly convex domain in C-n, n>1},
  language  = {en}
}
@book{KytmanovMyslivetsTarkhanov2002,
  author    = {Kytmanov, Alexander M. and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {Holomorphic lefschetz formula for manifolds with boundary},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {33 S.},
  year      = {2002},
  language  = {en}
}
@book{PrenovTarkhanov2001,
  author    = {Prenov, B. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Kernel Spikes of Singular Problems},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {16 S.},
  year      = {2001},
  language  = {en}
}
@book{KytmanovMyslivetsTarkhanov2003,
  author    = {Kytmanov, Alexander M. and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {Lefschetz theory for strictly pseudoconvex manifolds},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {16 S.},
  year      = {2003},
  language  = {en}
}
@book{TarkhanovVasilevski2005,
  author    = {Tarkhanov, Nikolai Nikolaevich and Vasilevski, Nikolai},
  title     = {Microlocal analysis of the Bochner-Martinelli Integral},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {9 S.},
  year      = {2005},
  language  = {en}
}
@book{ShlapunovTarkhanov2004,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Mixed problems with a parameter},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {28 S.},
  year      = {2004},
  language  = {en}
}
@article{ShlapunovTarkhanov2005,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Mixed problems with parameter},
  issn      = {1061-9208},
  year      = {2005},
  abstract  = {Let X be a smooth n-dimensional manifold and D be an open connected set in X with smooth boundary OD. Perturbing the Cauchy problem for an elliptic system Au = f in D with data on a closed set Gamma subset of partial derivativeD, we obtain a family of mixed problems depending on a small parameter epsilon > 0. Although the mixed problems are subjected to a noncoercive boundary condition on partial derivativeDF in general, each of them is uniquely solvable in an appropriate Hilbert space D-T and the corresponding family {u(epsilon)} of solutions approximates the solution of the Cauchy problem in D-T whenever the solution exists. We also prove that the existence of a solution to the Cauchy problem in D-T is equivalent to the boundedness of the family {u(epsilon)}. We thus derive a solvability condition for the Cauchy problem and an effective method of constructing the solution. Examples for Dirac operators in the Euclidean space R-n are treated. In this case, we obtain a family of mixed boundary problems for the Helmholtz equation},
  language  = {en}
}
@article{MeraShlapunovTarkhanov2019,
  author    = {Mera, Azal and Shlapunov, Alexander A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Navier-Stokes Equations for Elliptic Complexes},
  series = {Journal of Siberian Federal University. Mathematics \& Physics},
  volume    = {12},
  journal   = {Journal of Siberian Federal University. Mathematics \& Physics},
  number    = {1},
  publisher = {Sibirskij Federalʹnyj Universitet},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2019-12-1-3-27},
  pages     = {3 -- 27},
  year      = {2019},
  abstract  = {We continue our study of invariant forms of the classical equations of mathematical physics, such as the Maxwell equations or the Lam´e system, on manifold with boundary. To this end we interpret them in terms of the de Rham complex at a certain step. On using the structure of the complex we get an insight to predict a degeneracy deeply encoded in the equations. In the present paper we develop an invariant approach to the classical Navier-Stokes equations.},
  language  = {en}
}
@book{SchulzeTarkhanov2005,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {New algebras of boundary value problems for elliptic pseudodifferential operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {80 S.},
  year      = {2005},
  language  = {en}
}
@article{PalamodovTarkhanov2009,
  author    = {Palamodov, Victor and Tarkhanov, Nikolai Nikolaevich},
  title     = {Nonregular boundary problems for elliptic systems},
  issn      = {0188-7009},
  doi       = {10.1007/s00006-009-0159-2},
  year      = {2009},
  abstract  = {We discuss explicit boundary value problems for solutions of the Fueter equation in R-4 which are normally solvable. The results extend to nonlinear first order elliptic systems.},
  language  = {en}
}
@article{AlsaedyTarkhanov2014,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {Normally solvable nonlinear boundary value problems},
  series = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal},
  volume    = {95},
  journal   = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0362-546X},
  doi       = {10.1016/j.na.2013.09.024},
  pages     = {468 -- 482},
  year      = {2014},
  abstract  = {We investigate nonlinear problems which appear as Euler-Lagrange equations for a variational problem. They include in particular variational boundary value problems for nonlinear elliptic equations studied by F. Browder in the 1960s. We establish a solvability criterion of such problems and elaborate an efficient orthogonal projection method for constructing approximate solutions.},
  language  = {en}
}
@article{KytmanovMyslivetsTarkhanov2004,
  author    = {Kytmanov, Alexander M. and Myslivets, S. G. and Tarkhanov, Nikolai Nikolaevich},
  title     = {On a holomorphic Lefschetz formula in strictly pseudoconvex subdomains of complex manifolds},
  issn      = {1064-5616},
  year      = {2004},
  abstract  = {The classical Lefschetz formula expresses the number of fixed points of a continuous map f: M -> M in terms of the transformation induced by f on the cohomology of M. In 1966, Atiyah and Bott extended this formula to elliptic complexes over a compact closed manifold. In particular, they obtained a holomorphic Lefschetz formula on compact complex manifolds without boundary. Brenner and Shubin (1981, 1991) extended the Atiyah-Bott theory to compact manifolds with boundary. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, therefore the Atiyah- Bott theory is not applicable. Bypassing difficulties related to the boundary behaviour of Dolbeault cohomology, Donnelly and Fefferman (1986) obtained a formula for the number of fixed points in terms of the Bergman metric. The aim of this paper is to obtain a Lefschetz formula on relatively compact strictly pseudoconvex subdomains of complex manifolds X with smooth boundary, that is, to find the total Lefschetz number for a holomorphic endomorphism f(*) of the Dolbeault complex and to express it in terms of local invariants of the fixed points of f.},
  language  = {en}
}
@article{ShlapunovTarkhanov2013,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators},
  series = {Journal of differential equations},
  volume    = {255},
  journal   = {Journal of differential equations},
  number    = {10},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-0396},
  doi       = {10.1016/j.jde.2013.07.029},
  pages     = {3305 -- 3337},
  year      = {2013},
  abstract  = {We consider a Sturm-Liouville boundary value problem in a bounded domain D of R-n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on partial derivative D. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact selfadjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types. (C) 2013 Elsevier Inc. All rights reserved.},
  language  = {en}
}
@book{FedosovSchulzeTarkhanov2003,
  author    = {Fedosov, Boris V. and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {On index theorem for symplectic orbifolds},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {44 S.},
  year      = {2003},
  language  = {en}
}
@article{FedosovSchulzeTarkhanov2004,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {On the index theorem for symplectic orbifolds},
  issn      = {0373-0956},
  year      = {2004},
  abstract  = {We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula},
  language  = {en}
}
@article{GauthierTarkhanov2012,
  author    = {Gauthier, P. M. and Tarkhanov, Nikolai Nikolaevich},
  title     = {On the instability of the Riemann hypothesis for curves over finite fields},
  series = {Journal of approximation theory},
  volume    = {164},
  journal   = {Journal of approximation theory},
  number    = {4},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0021-9045},
  doi       = {10.1016/j.jat.2011.12.002},
  pages     = {504 -- 515},
  year      = {2012},
  abstract  = {We show that it is possible to approximate the zeta-function of a curve over a finite field by meromorphic functions which satisfy the same functional equation and moreover satisfy (respectively do not satisfy) an analog of the Riemann hypothesis. In the other direction, it is possible to approximate holomorphic functions by simple manipulations of such a zeta-function. No number theory is required to understand the theorems and their proofs, for it is known that the zeta-functions of curves over finite fields are very explicit meromorphic functions. We study the approximation properties of these meromorphic functions.},
  language  = {en}
}
@book{Tarkhanov2005,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Operator algebras related to the Bochner-Matinelli integral},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {15 S.},
  year      = {2005},
  language  = {en}
}
@book{MaergoizTarkhanov2006,
  author    = {Maergoiz, L. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Optimal recovery from finite set in banach spaces of entire functions},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {16 S.},
  year      = {2006},
  language  = {en}
}
@article{GarifullinevichSuleimanovTarkhanov2010,
  author    = {Garifullinevich, Rustem Nail and Suleimanov, Bulat Irekovich and Tarkhanov, Nikolai Nikolaevich},
  title     = {Phase shift in the Whitham zone for the Gurevich-Pitaevskii special solution of the Korteweg-de Vries equation},
  issn      = {0375-9601},
  doi       = {10.1016/j.physleta.2010.01.057},
  year      = {2010},
  abstract  = {We get the leading term of the Gurevich-Pitaevskii special solution of the KdV equation in the oscillation zone without using averaging methods.},
  language  = {en}
}