TY  - INPR
A1  - Fedchenko, Dmitry
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Class of Toeplitz Operators in Several Variables
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)17 
KW  - Cauchy data spaces
KW  - Laplace-Beltrami operator
KW  - Toeplitz operators
KW  - Fredholm property
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-68932
SN  - 2193-6943
ER  - 
TY  - JOUR
A1  - Fedchenko, Dmitry
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Class of Toeplitz Operators in Several Variables
JF  - Advances in applied Clifford algebras
N2  - 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.
KW  - Cauchy data spaces
KW  - Laplace-Beltrami operator
KW  - Toeplitz operators
KW  - Fredholm property
Y1  - 2015
U6  - https://doi.org/10.1007/s00006-015-0546-9
SN  - 0188-7009
SN  - 1661-4909
VL  - 25
IS  - 4
SP  - 811
EP  - 828
PB  - Springer
CY  - Basel
ER  - 
TY  - BOOK
A1  - Gauthier, P. M.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A covering proberty of the Riemann zeta-funktion
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2004
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A fixed point formula in one complex variable
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2003
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A general index formula on toric manifolds with conical point
Y1  - 2001
ER  - 
TY  - INPR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Hilbert boundary value problem for generalised Cauchy-Riemann equations
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 1 
KW  - Dirac operator
KW  - Clifford algebra
KW  - Riemann-Hilbert problem
KW  - Fredholm operator
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-86109
SN  - 2193-6943
VL  - 5
IS  - 1
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Hilbert Boundary Value Problem for Generalised Cauchy-Riemann Equations
JF  - Advances in applied Clifford algebras
N2  - 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.
KW  - Dirac operator
KW  - Clifford algebra
KW  - Riemann-Hilbert problem
KW  - Fredholm operators
Y1  - 2017
U6  - https://doi.org/10.1007/s00006-016-0676-8
SN  - 0188-7009
SN  - 1661-4909
VL  - 27
SP  - 931
EP  - 953
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Makhmudov, K. O.
A1  - Makhmudov, O. I.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A nonstandard Cauchy problem for the heat equation
JF  - Mathematical Notes
N2  - 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.
Y1  - 2017
U6  - https://doi.org/10.1134/S0001434617070264
SN  - 0001-4346
SN  - 1573-8876
VL  - 102
SP  - 250
EP  - 260
PB  - Pleiades Publ.
CY  - New York
ER  - 
TY  - INPR
A1  - Makhmudov, K. O.
A1  - Makhmudov, O. I.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A nonstandard Cauchy problem for the heat equation
N2  - We consider a Cauchy problem for the heat equation in a cylinder X x (0,T) over a domain X in the n-dimensional space 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015)11 
KW  - heat equation
KW  - Cauchy problem
KW  - Carleman formulas
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-83830
SN  - 2193-6943
VL  - 4
IS  - 11
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Rado theorem for p-harmonic functions
JF  - Boletin de la Sociedad Matemática Mexicana
N2  - 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.
KW  - Quasilinear equations
KW  - Removable sets
KW  - p-Laplace equation
Y1  - 2016
U6  - https://doi.org/10.1007/s40590-016-0109-7
SN  - 1405-213X
SN  - 2296-4495
VL  - 22
SP  - 461
EP  - 472
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Fedchenko, Dmitry
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Rado theorem for the porous medium equation
JF  - Boletin de la Sociedad Matemática Mexicana
N2  - 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.
KW  - Quasilinear equations
KW  - Removable sets
KW  - Porous medium equation
Y1  - 2017
U6  - https://doi.org/10.1007/s40590-017-0169-3
SN  - 1405-213X
SN  - 2296-4495
VL  - 24
IS  - 2
SP  - 427
EP  - 437
PB  - Springer
CY  - Cham
ER  - 
TY  - INPR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Radó theorem for p-harmonic functions
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 3 
KW  - Quasilinear equations
KW  - removable sets
KW  - p-Laplace Operator
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-71492
SN  - 2193-6943
VL  - 4
IS  - 3
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Fedchenko, Dmitry
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Radó Theorem for the Porous Medium Equation
T2  - Preprints des Instituts für Mathematik der Universität Potsdam
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 6 (2017) 1 
KW  - quasilinear equation
KW  - removable set
KW  - porous medium equation
Y1  - 2017
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-102735
VL  - 6
IS  - 1
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Polkovnikov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Riemann-Hilbert problem for the Moisil-Teodorescu system
N2  - In a bounded domain with smooth boundary in R^3 we consider the stationary Maxwell equations
for a function u with values in R^3 subject to a nonhomogeneous condition 
(u,v)_x = u_0 on
the boundary, where v is a given vector field and u_0 a function on the boundary. We specify this problem within the framework of the Riemann-Hilbert boundary value problems for the Moisil-Teodorescu system. This latter is proved to satisfy the Shapiro-Lopaniskij condition if an only if the vector v is at no point tangent to the boundary. The Riemann-Hilbert problem for the Moisil-Teodorescu system fails to possess an adjoint boundary value problem with respect to the Green formula, which satisfies the Shapiro-Lopatinskij condition. We develop the construction of Green formula to get a proper concept of adjoint boundary value problem.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 6 (2017) 3 
KW  - Dirac operator
KW  - Riemann-Hilbert problem
KW  - Fredholm operators
Y1  - 2017
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-397036
VL  - 6
IS  - 3
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A simple numerical approach to the Riemann hypothesis
N2  - The Riemann hypothesis is equivalent to the fact the the reciprocal function 1/zeta (s) extends from the interval (1/2,1) to an analytic function in the quarter-strip 1/2 < Re s < 1 and Im s > 0. Function theory allows one to rewrite the condition of analytic continuability in an elegant form amenable to numerical experiments.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 9 
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57645
SN  - 2193-6943
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A spectral theorem for deformation quantisation
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 4 
KW  - star product
KW  - WKB method
KW  - spectral theorem
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-72425
SN  - 2193-6943
VL  - 4
IS  - 4
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A variational approach to the Cauchy problem for nonlinear elliptic differential equations
N2  - 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.
Y1  - 2009
UR  - http://dx.doi.org/10.1515/jiip
U6  - https://doi.org/10.1515/Jiip.2009.037
SN  - 0928-0219
ER  - 
TY  - BOOK
A1  - Kytmanov, Alexander M.
A1  - Myslivets, Simona
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - An Asymptotic expansion of the Bochner-Martinelli integral
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgrupe Partielle Differentialgleichun
Y1  - 2001
SN  - 1437-339X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Makhmudov, Olimdjan
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - An extremal problem related to analytic continuation
N2  - We show that the usual variational formulation of the problem of analytic continuation from an arc on the boundary of a plane domain does not lead to a relaxation of this overdetermined problem. To attain such a relaxation, we bound the domain of the functional, thus changing the Euler equations.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 4 
KW  - Extremal problem
KW  - Euler equations
KW  - p-Laplace operator
KW  - mixed problems
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63634
ER  - 
TY  - INPR
A1  - Fedchenko, Dmitry
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - An index formula for Toeplitz operators
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3(2014)12 
KW  - Toeplitz operators
KW  - Fredholm property
KW  - index
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72499
SN  - 2193-6943
VL  - 3
IS  - 12
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Fedchenko, Dmitri
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - An index formula for Toeplitz operators
JF  - Complex variables and elliptic equations
N2  - 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.
KW  - Toeplitz operators
KW  - Fredholm property
KW  - index
KW  - Primary: 47B35
KW  - Secondary: 47L80
Y1  - 2015
U6  - https://doi.org/10.1080/17476933.2015.1050007
SN  - 1747-6933
SN  - 1747-6941
VL  - 60
IS  - 12
SP  - 1764
EP  - 1787
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  - 
TY  - INPR
A1  - Aizenberg, Lev A.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - An integral formula for the number of lattice points in a domain
N2  - Using the multidimensional logarithmic residue we show a simple formula for the difference between the number of integer points in a bounded domain of R^n and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 3 
KW  - logarithmic residue
KW  - lattice point
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70453
SN  - 2193-6943
VL  - 3
IS  - 3
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - An open mapping theorem for the Navier-Stokes equations
N2  - 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 Hölder 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 Fréchet 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 Hölder spaces.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016)10 
KW  - Navier-Stokes equations
KW  - weighted Hölder spaces
KW  - integral representation method
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-98687
SN  - 2193-6943
VL  - 5
IS  - 10
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Elin, Mark
A1  - Shoikhet, David
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Analytic semigroups of holomorphic mappings and composition operators
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 6 
KW  - nonlinear semigroup
KW  - composition operator
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-77914
SN  - 2193-6943
VL  - 4
IS  - 6
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Elin, Mark
A1  - Shoikhet, David
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Analytic Semigroups of Holomorphic Mappings and Composition Operators
JF  - Computational Methods and Function Theory
N2  - 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.
KW  - Non-linear semigroups
KW  - Composition operators
KW  - Analytic extension
KW  - Holomorphic mappings
Y1  - 2017
U6  - https://doi.org/10.1007/s40315-017-0227-x
SN  - 1617-9447
SN  - 2195-3724
VL  - 18
IS  - 2
SP  - 269
EP  - 294
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - BOOK
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Anisotropic edge problems
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2002
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Asymptotic expansions at nonsymmetric cuspidal points
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 7 
KW  - the Dirichlet problem
KW  - singular point
KW  - asymptotic expansion
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-78199
SN  - 2193-6943
VL  - 4
IS  - 7
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Antoniouk, Alexandra Viktorivna
A1  - Kiselev, Oleg M.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Asymptotic Solutions of the Dirichlet Problem for the Heat Equation at a Characteristic Point
JF  - Ukrainian mathematical journal
N2  - 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.
Y1  - 2015
U6  - https://doi.org/10.1007/s11253-015-1038-8
SN  - 0041-5995
SN  - 1573-9376
VL  - 66
IS  - 10
SP  - 1455
EP  - 1474
PB  - Springer
CY  - New York
ER  - 
TY  - INPR
A1  - Antoniouk, Alexandra Viktorivna
A1  - Kiselev, Oleg
A1  - Stepanenko, Vitaly
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point
N2  - The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)25 
KW  - Heat equation
KW  - the first boundary value problem
KW  - characteristic boundary point
KW  - cusp
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-61987
ER  - 
TY  - JOUR
A1  - Glebov, Sergei
A1  - Kiselev, Oleg
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Autoresonance in a dissipative system
N2  - 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.
Y1  - 2010
UR  - http://iopscience.iop.org/1751-8121/
U6  - https://doi.org/10.1088/1751-8113/43/21/215203
SN  - 1751-8113
ER  - 
TY  - INPR
A1  - Fedchenko, Dmitry
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Boundary value problems for elliptic complexes
N2  - The aim of this paper is to bring together two areas which are of great importance for the study of overdetermined boundary value problems. The first area is homological algebra which is the main tool in constructing the formal theory of overdetermined problems. And the second area is the global calculus of pseudodifferential operators which allows one to develop explicit analysis.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 3 
KW  - elliptic complexes
KW  - Fredholm property
KW  - index
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-86705
SN  - 2193-6943
VL  - 5
IS  - 3
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Rabinovich, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Boundary value problems in oscillating cuspidal wedges
N2  - 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
Y1  - 2004
SN  - 0035-7596
ER  - 
TY  - JOUR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Cancellation of a Publication
JF  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2008
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Grudsky, Serguey
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Conformal reduction of boundary problems for harmonic functions in a plane domain with strong singularities on the boundary
N2  - We consider the Dirichlet, Neumann and Zaremba problems for harmonic functions in a bounded plane domain with nonsmooth boundary. The boundary curve belongs to one of the following three classes: sectorial curves, logarithmic spirals and spirals of power type. To study the problem we apply a familiar method of Vekua-Muskhelishvili which consists in using a conformal mapping of the unit disk onto the domain to pull back the problem to a boundary problem for harmonic functions in the disk. This latter is reduced in turn to a Toeplitz operator equation on the unit circle with symbol bearing discontinuities of second kind. We develop a constructive invertibility theory for Toeplitz operators and thus derive solvability conditions as well as explicit formulas for solutions.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)10 
KW  - singular integral equations
KW  - nonsmooth curves
KW  - boundary value problems
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57745
ER  - 
TY  - INPR
A1  - Vasiliev, Serguei
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Construction of series of perfect lattices by layer superposition
N2  - We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016)11 
KW  - lattice packing and covering
KW  - polyhedra and polytopes
KW  - regular figures
KW  - division of spaces
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-100591
SN  - 2193-6943
VL  - 5
IS  - 11
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Fedosov, Boris
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Deformation quantisation and boundary value problems
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 5 
KW  - symplectic manifold
KW  - star product
KW  - trace
KW  - index
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-77150
SN  - 2193-6943
VL  - 4
IS  - 5
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Deformation quantization and boundary value problems
JF  - International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis & topology
N2  - 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.
KW  - Symplectic manifold
KW  - star product
KW  - trace
KW  - index
Y1  - 2016
U6  - https://doi.org/10.1142/S0219887816500079
SN  - 0219-8878
SN  - 1793-6977
VL  - 13
SP  - 176
EP  - 195
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - INPR
A1  - Dyachenko, Evgueniya
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Degeneration of boundary layer at singular points
N2  - We study the Dirichlet problem in a bounded plane domain for the heat equation with small parameter multiplying the derivative in t. The behaviour of solution at characteristic points of the boundary is of special interest. The behaviour is well understood if a characteristic line is tangent to the boundary with contact degree at least 2. We allow the boundary to not only have contact of degree less than 2 with a characteristic line but also a cuspidal singularity at a characteristic point. We construct an asymptotic solution of the problem near the characteristic point to describe how the boundary layer degenerates.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)23 
KW  - Heat equation
KW  - Dirichlet problem
KW  - characteristic points
KW  - boundary layer
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60135
ER  - 
TY  - JOUR
A1  - Bagderina, Yulia Yu.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Differential invariants of a class of Lagrangian systems with two degrees of freedom
JF  - Journal of mathematical analysis and applications
KW  - Equivalence
KW  - Differential invariant
KW  - Euler-Lagrange equations
Y1  - 2014
U6  - https://doi.org/10.1016/j.jmaa.2013.08.015
SN  - 0022-247X
SN  - 1096-0813
VL  - 410
IS  - 2
SP  - 733
EP  - 749
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - INPR
A1  - Bagderina, Yulia Yu.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Differential invariants of a class of Lagrangian systems with two degrees of freedom
N2  - We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 2 
KW  - equivalence
KW  - invariant
KW  - Euler-Lagrange equations
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63129
ER  - 
TY  - BOOK
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Duality by reproducing kernels
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2001
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Sultanov, Oskar
A1  - Kalyakin, Leonid
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Elliptic perturbations of dynamical systems with a proper node
N2  - The paper is devoted to asymptotic analysis of the Dirichlet problem for a second order partial differential equation containing a small parameter multiplying the highest order derivatives. It corresponds to a small perturbation of a dynamical system having a stationary solution in the domain. We focus on the case where the trajectories of the system go into the domain and the stationary solution is a proper node.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 4 
KW  - dynamical system
KW  - singular perturbation
KW  - asymptotic methods
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70460
SN  - 2193-6943
VL  - 3
IS  - 4
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Kytmanov, Alexander M.
A1  - Myslivets, Simona
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Elliptic problems for the Dolbeault complex
N2  - 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
Y1  - 2005
SN  - 0025-584X
ER  - 
TY  - BOOK
A1  - Krupchyk, K.
A1  - Tarkhanov, Nikolai Nikolaevich
A1  - Tuomela, J.
T1  - Elliptic quasicomplexes in boutet de monvel algebra
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2006
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Makhmudo, K. O.
A1  - Makhmudov, O. I.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Equations of Maxwell type
JF  - Journal of mathematical analysis and applications
N2  - 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.
KW  - Electromagnetic waves
KW  - Scattering
KW  - Elliptic complex
KW  - Green formulas
KW  - Stratton-Chu formulas
KW  - Cauchy problem
Y1  - 2011
U6  - https://doi.org/10.1016/j.jmaa.2011.01.012
SN  - 0022-247X
VL  - 378
IS  - 1
SP  - 64
EP  - 75
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - BOOK
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Euler characteristic of Fredholm quasicomplexes
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2006
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Fixed point formula for holomorphic functions
N2  - 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
Y1  - 2004
SN  - 0002-9939
ER  - 
TY  - JOUR
A1  - Glebov, Sergei
A1  - Kiselev, Oleg
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Forced nonlinear resonance in a system of coupled oscillators
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - 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.
Y1  - 2011
U6  - https://doi.org/10.1063/1.3578047
SN  - 1054-1500
VL  - 21
IS  - 2
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Formal poincare lemma
JF  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2007
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Krupchyk, K.
A1  - Tarkhanov, Nikolai Nikolaevich
A1  - Tuomela, J.
T1  - Generalised elliptic boundary problems
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2005
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  -