TY  - INPR
A1  - Aizenberg, Lev A.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Bohr phenomenon for elliptic equations
N2  - In 1914 Bohr proved that there is an r ∈ (0, 1) such that if a power series converges in the unit disk and its sum has modulus less than 1 then, for |z| < r, the sum of absolute values of its terms is again less than 1. Recently analogous results were obtained for functions of several variables. The aim of this paper is to comprehend the theorem of Bohr in the context of solutions to second order elliptic equations meeting the maximum principle.
T3  - Preprint - (1999) 18 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25547
ER  - 
TY  - INPR
A1  - Rabinovich, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A calculus of boundary value problems in domains with Non-Lipschitz Singular Points
N2  - The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points.
T3  - Preprint - (1997) 09 
KW  - pseudodifferential operators
KW  - boundary value problems
KW  - manifolds with cusps
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24957
ER  - 
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  - INPR
A1  - Gauthier, Paul M.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A covering property of the Riemann zeta-function
N2  - For each compact subset K of the complex plane C which does not surround zero, the Riemann surface Sζ of the Riemann zeta function restricted to the critical half-strip 0 < Rs < 1/2 contains infinitely many schlicht copies of K lying ‘over’ K. If Sζ also contains at least one such copy, for some K which surrounds zero, then the Riemann hypothesis fails.
T3  - Preprint - (2004) 03 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26683
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  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A fixed point formula in one complex variable
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 kernal of this domain. The Lefschetz number is proved to be the sum of 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.
T3  - Preprint - (2003) 01 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26495
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  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A general index formula on tropic manifolds with conical points
N2  - We solve the index problem for general elliptic pseudodifferential operators on toric manifolds with conical points.
T3  - Preprint - (1999) 15 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25501
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  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Lefschetz fixed point formula in the relative elliptic theory
N2  - A version of the classical Lefschetz fixed point formula is proved for the cohomology of the cone of a cochain mapping of elliptic complexes. As a particular case we show a Lefschetz formula for the relative de Rham cohomology.
T3  - Preprint - (1998) 01 
KW  - elliptic complexes
KW  - relative cohomology
KW  - Lefschetz number
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25159
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  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A remark on the index of symmetric operators
N2  - We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol.
T3  - Preprint - (1998) 04 
KW  - manifolds with singularities
KW  - differential operators
KW  - index
KW  - 'eta' invariant
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25169
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  -