@unpublished{AizenbergTarkhanov1999, author = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich}, title = {A Bohr phenomenon for elliptic equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25547}, year = {1999}, abstract = {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Bohr in the context of solutions to second order elliptic equations meeting the maximum principle.}, language = {en} } @unpublished{RabinovichSchulzeTarkhanov1997, author = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A calculus of boundary value problems in domains with Non-Lipschitz Singular Points}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24957}, year = {1997}, abstract = {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property of a boundary value problem and derive estimates of solutions close to singular points.}, language = {en} } @unpublished{FedchenkoTarkhanov2013, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {A Class of Toeplitz Operators in Several Variables}, issn =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} } @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} } @unpublished{GauthierTarkhanov2004, author = {Gauthier, Paul M. and Tarkhanov, Nikolai Nikolaevich}, title = {A covering property of the Riemann zeta-function}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26683}, year = {2004}, abstract = {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.}, 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} } @unpublished{Tarkhanov2003, author = {Tarkhanov, Nikolai Nikolaevich}, title = {A fixed point formula in one complex variable}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26495}, year = {2003}, 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 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.}, 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} } @unpublished{FedosovSchulzeTarkhanov1999, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A general index formula on tropic manifolds with conical points}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25501}, year = {1999}, abstract = {We solve the index problem for general elliptic pseudodifferential operators on toric manifolds with conical points.}, language = {en} }