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1	An index formula for Toeplitz operators Fedchenko, Dmitry, Tarkhanov, Nikolai January 2014 (has links) 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. Toeplitz operators Fredholm property index Mathematics
2	A Class of Toeplitz Operators in Several Variables Fedchenko, Dmitry, Tarkhanov, Nikolai January 2013 (has links) 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. Cauchy data spaces Laplace-Beltrami operator Toeplitz operators Fredholm property Mathematics
3	A Lefschetz fixed point theorem for manifolds with conical singularities Nazaikinskii, Vladimir, Schulze, Bert-Wolfgang, Sternin, Boris, Shatalov, Victor January 1997 (has links) We establish an Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singular points. elliptic operator Fredholm property conical singularities pseudo-diferential operators Lefschetz fixed point formula regularizer Mathematics
4	Spectral boundary value problems and elliptic equations on singular manifolds Schulze, Bert-Wolfgang, Nazaikinskii, Vladimir, Sternin, Boris, Shatalov, Victor January 1997 (has links) For elliptic operators on manifolds with boundary, we define spectral boundary value problems, which generalize the Atiyah-Patodi-Singer problem to the case of nonhomogeneous boundary conditions, operators of arbitrary order, and nonself-adjoint conormal symbols. The Fredholm property is proved and equivalence with certain elliptic equations on manifolds with conical singularities is established. APS problem spectral resolution nonhomogeneous boundary value problems Fredholm property Mathematics
5	On the invariant index formulas for spectral boundary value problems Savin, Anton, Schulze, Bert-Wolfgang, Sternin, Boris January 1998 (has links) In the paper we study the possibility to represent the index formula for spectral boundary value problems as a sum of two terms, the first one being homotopy invariant of the principal symbol, while the second depends on the conormal symbol of the problem only. The answer is given in analytical, as well as in topological terms. spectral boundary value problems Fredholm property index of elliptic operator Chern character Atiyah-Patodi-Singer theory Mathematics
6	A semiclassical quantization on manifolds with singularities and the Lefschetz Formula for Elliptic Operators Schulze, Bert-Wolfgang, Nazaikinskii, Vladimir, Sternin, Boris January 1998 (has links) For general endomorphisms of elliptic complexes on manifolds with conical singularities, the semiclassical asymptotics of the Atiyah-Bott-Lefschetz number is calculated in terms of fixed points of the corresponding canonical transformation of the symplectic space. elliptic operator Fredholm property conical singularities pseudodiferential operators Lefschetz fixed point formula regularizer Mathematics
7	Elliptic operators in subspaces Savin, Anton, Schulze, Bert-Wolfgang, Sternin, Boris January 2000 (has links) We construct elliptic theory in the subspaces, determined by pseudodifferential projections. The finiteness theorem as well as index formula are obtained for elliptic operators acting in the subspaces. Topological (K-theoretic) aspects of the theory are studied in detail. pseudodifferential subspaces elliptic operators in subspaces Fredholm property index K-theory problem of classification Mathematics

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