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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
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.
Received: 28.03.2023 Revised: 28.03.2023 Accepted: 02.04.2023
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
Linking options:
https://www.mathnet.ru/eng/faa4108https://doi.org/10.4213/faa4108 https://www.mathnet.ru/eng/faa/v57/i2/p106
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Abstract page: | 191 | Full-text PDF : | 26 | References: | 28 | First page: | 10 |
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