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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 3 scientific papers (total in 3 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
Full-text PDF (464 kB) Citations (3)
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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 L2(μ) with kernel ρ. 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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\by A.~M.~Vershik, F.~V.~Petrov
\paper Limit spectral measures of matrix distributions of metric triples
\jour Funktsional. Anal. i Prilozhen.
\yr 2023
\vol 57
\issue 2
\pages 106--110
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\crossref{https://doi.org/10.4213/faa4108}
\transl
\jour Funct. Anal. Appl.
\yr 2023
\vol 57
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\pages 169--172
\crossref{https://doi.org/10.1134/S0016266323020089}
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  • https://www.mathnet.ru/eng/faa4108
  • https://doi.org/10.4213/faa4108
  • https://www.mathnet.ru/eng/faa/v57/i2/p106
    • This publication is cited in the following 3 articles:
    1. Tianyu Ma, Eugene Stepanov, “On eigenvalues and eigenfunctions of the operators defining multidimensional scaling on some symmetric spaces”, Information and Inference: A Journal of the IMA, 14:1 (2025)  crossref
    2. A. M. Vershik, G. A. Veprev, P. B. Zatitskii, “Dynamics of metrics in measure spaces and scaling entropy”, Russian Math. Surveys, 78:3 (2023), 443–499  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. A. M. Vershik, “Classification of measurable functions of several variables and matrix distributions”, Funct. Anal. Appl., 57:4 (2023), 303–313  mathnet  crossref  crossref  isi
    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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