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Funktsional'nyi Analiz i ego Prilozheniya, 2023, Volume 57, Issue 2, Pages 106–110
DOI: https://doi.org/10.4213/faa4108 (Mi faa4108) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Brief communications

Limit spectral measures of matrix distributions of metric triples

A. M. Vershikabc, F. V. Petrovab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Saint Petersburg State University
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
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DOI: https://doi.org/10.4213/faa4108
Abstract: The notion of the limit spectral measure of a metric triple (i.e., a metric measure space) is defined. If the metric is square integrable, then the limit spectral measure is deterministic and coincides with the spectrum of the integral operator on $L^2(\mu)$ with kernel $\rho$. An example in which there is no deterministic spectral measure is constructed.
Keywords: metric triples, spectra, limit measures, Cauchy distribution.
Funding agency Grant number
Russian Science Foundation 21-11-00152
Received: 28.03.2023
Revised: 28.03.2023
Accepted: 02.04.2023
English version:
Functional Analysis and Its Applications, 2023, Volume 57, Issue 2, Pages 169–172
DOI: https://doi.org/10.1134/S0016266323020089
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. M. Vershik, F. V. Petrov, “Limit spectral measures of matrix distributions of metric triples”, Funktsional. Anal. i Prilozhen., 57:2 (2023), 106–110; Funct. Anal. Appl., 57:2 (2023), 169–172
Citation in format AMSBIB
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\paper Limit spectral measures of matrix distributions of metric triples
\jour Funktsional. Anal. i Prilozhen.
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\vol 57
\issue 2
\pages 106--110
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\jour Funct. Anal. Appl.
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\issue 2
\pages 169--172
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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