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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 311, Pages 241–249
DOI: https://doi.org/10.4213/tm4118 (Mi tm4118) 		 
Trace Class Toeplitz Operators with Singular Symbols

Grigori V. Rozenblumab, Nikolai L. Vasilevskic

a Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Gothenburg, Sweden
b Faculty of Physics, St. Petersburg State University, Petergof, Ul'yanovskaya ul. 1, St. Petersburg, 198504 Russia
c Departamento de Matemáticas, Cinvestav, Av. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, Ciudad de México, CP 07360, Mexico
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DOI: https://doi.org/10.4213/tm4118
Abstract: We provide sufficient conditions for Toeplitz operators with distributional symbols acting on the Bergman space on the unit disk to be trace class. The Berezin transform of distributions, introduced in the paper, yields a formula for the trace. Several instructive examples are also given.
Keywords: Bergman space, Toeplitz operators, distributional symbol.
Funding agency Grant number
Russian Science Foundation 20-11-20032
The work of the first author is supported by the Russian Science Foundation under grant 20-11-20032.
Received: February 16, 2020
Revised: April 7, 2020
Accepted: June 24, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 311, Pages 225–232
DOI: https://doi.org/10.1134/S0081543820060140
Bibliographic databases:
Document Type: Article
UDC: 517.983.26
MSC: 47A75 (primary), 58J50 (secondary)
Language: Russian
Citation: Grigori V. Rozenblum, Nikolai L. Vasilevski, “Trace Class Toeplitz Operators with Singular Symbols”, Analysis and mathematical physics, Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev, Trudy Mat. Inst. Steklova, 311, Steklov Math. Inst., Moscow, 2020, 241–249; Proc. Steklov Inst. Math., 311 (2020), 225–232
Citation in format AMSBIB
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\paper Trace Class Toeplitz Operators with Singular Symbols
\inbook Analysis and mathematical physics
\bookinfo Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 311
\pages 241--249
\publ Steklov Math. Inst.
\publaddr Moscow
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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