Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 193, Pages 142–152
DOI: https://doi.org/10.36535/0233-6723-2021-193-142-152 (Mi into808) 		 
An abstract formula for regularized traces of discrete operators and its applications

N. G. Tomin, I. V. Tomina

Ivanovo State Power University
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DOI: https://doi.org/10.36535/0233-6723-2021-193-142-152
Abstract: In this paper, we prove an abstract formula for regularized traces of discrete operators in a separable Hilbert space. This formula is a generalization of the formula for the first regularized trace to the case of higher-order traces. We also discuss applications of the formula obtained to a wide class of discrete operators acting in the Bergman space that are generalizations of the Gribov operator from Reggeon field theory.
Keywords: Hilbert space, discrete operator, linear non-self-adjoint operator, spectral theory, regularized trace formula, Bergman space, Reggeon field theory, Gribov operator.
Document Type: Article
UDC: 517.94, 517.984, 517.951
MSC: 35P20, 47A10, 47B37, 32K15
Language: Russian
Citation: N. G. Tomin, I. V. Tomina, “An abstract formula for regularized traces of discrete operators and its applications”, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 193, VINITI, Moscow, 2021, 142–152
Citation in format AMSBIB
\Bibitem{TomTom21}
\by N.~G.~Tomin, I.~V.~Tomina
\paper An abstract formula for regularized traces of discrete operators and its applications
\inbook Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 4
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 193
\pages 142--152
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into808}
\crossref{https://doi.org/10.36535/0233-6723-2021-193-142-152}
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