@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{KytmanovMyslivetsTarkhanov2004, author = {Kytmanov, Alexander M. and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich}, title = {Zeta-function of a nonlinear system}, 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{KytmanovMyslivetsTarkhanov2004, author = {Kytmanov, Alexander M. and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich}, title = {Power sums of roots of a nonlinear system}, 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 = {12 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 On compact complex manifolds with boundary the Dolbeault complex is not elliptic, hence the Atiyah- Bott theory is no longer applicable.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} } @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{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{Kytmanov2001, author = {Kytmanov, Alexander M.}, title = {Elliptic problems for the dolbeault complex}, 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 = {37 S.}, year = {2001}, 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} } @book{KytmanovMyslivecTarchanov2000, author = {Kytmanov, Alexander M. and Myslivec, S. and Tarchanov, Nikolaj N.}, title = {Removable singularities of CR functions on singular boundaries}, 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 = {29 S.}, year = {2000}, language = {en} }