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Your search keyword '"Mirotin, Adolf R."' showing total 10 results
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10 results on '"Mirotin, Adolf R."'

1. TO THE SPECTRAL THEORY OF DISCRETE HAUSDORFF OPERATORS

Author

Mirotin, Adolf R.

Subjects
Mathematics
Abstract

We show that under an arithmetic condition the spectrum of a bounded multidimensional discrete Hausdorff operator in the Lebesgue space is an annulus (or a disc) centered at the origin, provided the perturbation matrices commute and are either positive or negative definite. Conditions for a point spectrum of such an operator to be empty are given and its norm is computed., Author(s): Adolf R. Mirotin [sup.1] [sup.2] Author Affiliations: (1) https://ror.org/03h5rdc49, grid.440509.c, 0000 0001 1503 4316, Department of Mathematics and Programming Technologies, Francisk Skorina Gomel State University, , Sovietskaya, 104, 246019, [...]

Published
2023
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2. Lifshitz-Krein trace formula for Hirsch functiuonal calculus on Banach spaces

Author

Mirotin, Adolf R

Subjects
Mathematics - Functional Analysis, Primary 47A56, Secondary 47A55, 47B10, 47L20
Abstract

We give a simple definition of a spectral shift function for pairs of nonpositive operators on Banach spaces and prove trace formulas of Lifshitz-Kre\u{\i}n type for a perturbation of an operator monotonic (negative complete Bernstein) function of negative and nonpositive operators on Banach spaces induced by nuclear perturbation of an operator argument. The Lipschitzness of such functions is also investigated. The results may be regarded as a contribution to a perturbation theory for Hirsch functional calculus.

Published
2018

10. Fredholm and spectral properties of Toeplitz operators on spaces over ordered groups

Author

Mirotin, Adolf R

Abstract

We consider Toeplitz operators on the spaces , , associated with a compact connected Abelian group whose character group is ordered and, in the case of total order, prove a theorem on the Fredholm index for those operators which have continuous symbols which generalizes the classical Gohberg-Krein theorem. The results thus obtained are applied to the spectral theory of Toeplitz operators and examples where the index is evaluated explicitly are considered.

Published
2011
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