@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}
}
@unpublished{LyTarkhanov2013,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {Generalised Beltrami equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67416},
  year      = {2013},
  abstract  = {We enlarge the class of Beltrami equations by developping a stability theory for the sheaf of solutions of an overdetermined elliptic system of first order homogeneous partial differential equations with constant coefficients in the Euclidean space.},
  language  = {en}
}
@unpublished{LyTarkhanov2015,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Rad{\´o} theorem for p-harmonic functions},
  volume    = {4},
  number    = {3},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-71492},
  pages     = {10},
  year      = {2015},
  abstract  = {Let A be a nonlinear differential operator on an open set X in 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 the complement of S 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}
}
@unpublished{LyTarkhanov2015,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {Asymptotic expansions at nonsymmetric cuspidal points},
  volume    = {4},
  number    = {7},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-78199},
  pages     = {11},
  year      = {2015},
  abstract  = {We study asymptotics of solutions to the Dirichlet problem in a domain whose boundary contains a nonsymmetric conical point. We establish a complete asymptotic expansion of solutions near the singular point.},
  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{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}
}
@unpublished{ShlapunovTarkhanov2016,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {An open mapping theorem for the Navier-Stokes equations},
  volume    = {5},
  number    = {10},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-98687},
  pages     = {80},
  year      = {2016},
  abstract  = {We consider the Navier-Stokes equations in the layer R^n x [0,T] over R^n with finite T > 0. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to a nonlinear Fredholm equation of the form (I+K) u = f, where K is a compact continuous operator in anisotropic normed H{\"o}lder spaces weighted at the point at infinity with respect to the space variables. Actually, the weight function is included to provide a finite energy estimate for solutions to the Navier-Stokes equations for all t in [0,T]. On using the particular properties of the de Rham complex we conclude that the Fr{\´e}chet derivative (I+K)' is continuously invertible at each point of the Banach space under consideration and the map I+K is open and injective in the space. In this way the Navier-Stokes equations prove to induce an open one-to-one mapping in the scale of H{\"o}lder spaces.},
  language  = {en}
}
@unpublished{FedosovTarkhanov2015,
  author    = {Fedosov, Boris and Tarkhanov, Nikolai Nikolaevich},
  title     = {Deformation quantisation and boundary value problems},
  volume    = {4},
  number    = {5},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77150},
  pages     = {27},
  year      = {2015},
  abstract  = {We describe a natural construction of deformation quantisation 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}
}
@unpublished{ElinShoikhetTarkhanov2015,
  author    = {Elin, Mark and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich},
  title     = {Analytic semigroups of holomorphic mappings and composition operators},
  volume    = {4},
  number    = {6},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77914},
  pages     = {30},
  year      = {2015},
  abstract  = {In this paper we study 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. We also provide a brief review around this topic.},
  language  = {en}
}
@unpublished{FedchenkoTarkhanov2017,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Rad{\´o} Theorem for the Porous Medium Equation},
  series = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam},
  volume    = {6},
  journal   = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam},
  number    = {1},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102735},
  pages     = {12},
  year      = {2017},
  abstract  = {We prove that each locally Lipschitz continuous function satisfying the porous medium equation away from the set of its zeroes is actually a weak solution of this equation in the whole domain.},
  language  = {en}
}
@unpublished{ShlapunovTarkhanov2017,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Golusin-Krylov Formulas in Complex Analysis},
  series = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam},
  volume    = {6},
  journal   = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam},
  number    = {2},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102774},
  pages     = {25},
  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}
}
@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{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{MakhmudovNiyozovTarkhanov2006,
  author    = {Makhmudov, O. I. and Niyozov, I. E. and Tarkhanov, Nikolai Nikolaevich},
  title     = {The cauchy problem of couple-stress elasticity},
  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      = {2006},
  language  = {en}
}
@book{KytmanovMyslivetsTarkhanov2006,
  author    = {Kytmanov, Alexander M. and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {The bochner-martinelli integral on surfaces with singular points},
  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     = {23 S.},
  year      = {2006},
  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}
}
@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}
}
@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}
}
@unpublished{VasilievTarkhanov2016,
  author    = {Vasiliev, Serguei and Tarkhanov, Nikolai Nikolaevich},
  title     = {Construction of series of perfect lattices by layer superposition},
  volume    = {5},
  number    = {11},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100591},
  pages     = {11},
  year      = {2016},
  abstract  = {We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes.},
  language  = {en}
}
@book{Tarkhanov2005,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Unitary solutions of paratial differential equations},
  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     = {35 S.},
  year      = {2005},
  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}
}
@book{BermanTarkhanov2004,
  author    = {Berman, Gennady and Tarkhanov, Nikolai Nikolaevich},
  title     = {The dynamics of four wave interactions},
  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     = {25 S.},
  year      = {2004},
  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}
}
@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}
}
@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{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{Tarkhanov2005,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Root functions of elliptic boundary problems in domains with conic points on the 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     = {20 S.},
  year      = {2005},
  language  = {en}
}
@book{AizenbergTarkhanov2005,
  author    = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Stable expansions in homogeneous polynomials},
  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     = {23 S.},
  year      = {2005},
  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}
}
@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}
}
@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{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}
}
@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{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}
}
@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}
}
@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}
}
@unpublished{KytmanovMyslivetsTarkhanov1999,
  author    = {Kytmanov, Alexander and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {Analytic representation of CR Functions on hypersurfaces with singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25631},
  year      = {1999},
  abstract  = {We prove a theorem on analytic representation of integrable CR functions on hypersurfaces with singular points. Moreover, the behaviour of representing analytic functions near singular points is investigated. We are aimed at explaining the new effect caused by the presence of a singularity rather than at treating the problem in full generality.},
  language  = {en}
}
@unpublished{ShlapunovTarkhanov2004,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Mixed problems with a parameter},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26677},
  year      = {2004},
  abstract  = {Let X be a smooth n -dimensional manifold and D be an open connected set in X with smooth boundary ∂D. Perturbing the Cauchy problem for an elliptic system Au = f in D with data on a closed set Γ ⊂ ∂D we obtain a family of mixed problems depending on a small parameter ε > 0. Although the mixed problems are subject to a non-coercive boundary condition on ∂D\Γ in general, each of them is uniquely solvable in an appropriate Hilbert space DT and the corresponding family {uε} of solutions approximates the solution of the Cauchy problem in DT whenever the solution exists. We also prove that the existence of a solution to the Cauchy problem in DT is equivalent to the boundedness of the family {uε}. We thus derive a solvability condition for the Cauchy problem and an effective method of constructing its solution. Examples for Dirac operators in the Euclidean space Rn are considered. In the latter case we obtain a family of mixed boundary problems for the Helmholtz equation.},
  language  = {en}
}
@unpublished{BermanTarkhanov2004,
  author    = {Berman, Gennady and Tarkhanov, Nikolai Nikolaevich},
  title     = {Quantum dynamics in the Fermi-Pasta-Ulam problem},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26695},
  year      = {2004},
  abstract  = {We study the dynamics of four wave interactions in a nonlinear quantum chain of oscillators under the "narrow packet" approximation. We determine the set of times for which the evolution of decay processes is essentially specified by quantum effects. Moreover, we highlight the quantum increment of instability.},
  language  = {en}
}
@unpublished{KytmanovMyslivetsTarkhanov2004,
  author    = {Kytmanov, Aleksandr and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {Power sums of roots of a nonlinear system},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26788},
  year      = {2004},
  abstract  = {For a system of meromorphic functions f = (f1, . . . , fn) in Cn, an explicit formula is given for evaluating negative power sums of the roots of the nonlinear system f(z) = 0.},
  language  = {en}
}
@unpublished{KytmanovMyslivetsTarkhanov2004,
  author    = {Kytmanov, Aleksandr and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {Zeta-function of a nonlinear system},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26795},
  year      = {2004},
  abstract  = {Given a system of entire functions in Cn with at most countable set of common zeros, we introduce the concept of zeta-function associated with the system. Under reasonable assumptions on the system, the zeta-function is well defined for all s ∈ Zn with sufficiently large components. Using residue theory we get an integral representation for the zeta-function which allows us to construct an analytic extension of the zeta-function to an infinite cone in Cn.},
  language  = {en}
}
@unpublished{FedchenkoTarkhanov2014,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {An index formula for Toeplitz operators},
  volume    = {3},
  number    = {12},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72499},
  pages     = {24},
  year      = {2014},
  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 of Euclidean space with infinitely differentiable boundary.},
  language  = {en}
}
@unpublished{AlsaedyTarkhanov2012,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {The method of Fischer-Riesz equations for elliptic boundary value problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-61792},
  year      = {2012},
  abstract  = {We develop the method of Fischer-Riesz equations for general boundary value problems elliptic in the sense of Douglis-Nirenberg. To this end we reduce them to a boundary problem for a (possibly overdetermined) first order system whose classical symbol has a left inverse. For such a problem there is a uniquely determined boundary value problem which is adjoint to the given one with respect to the Green formula. On using a well elaborated theory of approximation by solutions of the adjoint problem, we find the Cauchy data of solutions of our problem.},
  language  = {en}
}
@unpublished{FedchenkoTarkhanov2013,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Class of Toeplitz Operators in Several Variables},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-68932},
  year      = {2013},
  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}
}
@unpublished{AlsaedyTarkhanov2015,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {Weak boundary values of solutions of Lagrangian problems},
  volume    = {4},
  number    = {2},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72617},
  pages     = {24},
  year      = {2015},
  abstract  = {We define weak boundary values of solutions to those nonlinear differential equations which appear as Euler-Lagrange equations of variational problems. As a result we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to the study of Lagrangian problems.},
  language  = {en}
}
@unpublished{Tarkhanov2015,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {A spectral theorem for deformation quantisation},
  volume    = {4},
  number    = {4},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-72425},
  pages     = {8},
  year      = {2015},
  abstract  = {We present a construction of the eigenstate at a noncritical level of the Hamiltonian function. Moreover, we evaluate the contributions of Morse critical points to the spectral decomposition.},
  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{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}
}
@article{MeraStepanenkoTarkhanov2018,
  author    = {Mera, Azal and Stepanenko, Vitaly A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Successive approximation for the inhomogeneous burgers equation},
  series = {Journal of Siberian Federal University : Mathematics \& Physics},
  volume    = {11},
  journal   = {Journal of Siberian Federal University : Mathematics \& Physics},
  number    = {4},
  publisher = {Siberian Federal University},
  address   = {Krasnoyarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2018-11-4-519-531},
  pages     = {519 -- 531},
  year      = {2018},
  abstract  = {The inhomogeneous Burgers equation is a simple form of the Navier-Stokes equations. From the analytical point of view, the inhomogeneous form is poorly studied, the complete analytical solution depending closely on the form of the nonhomogeneous term.},
  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}
}