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Bulletin of Irkutsk State University. Series Mathematics, 2021, Volume 37, Pages 77–92
DOI: https://doi.org/10.26516/1997-7670.2021.37.77 (Mi iigum461) 		 
Integro-differential equations and functional analysis

On distributions of trigonometric polynomials in Gaussian random variables

G. I. Zelenovab

a Lomonosov Moscow State University, Moscow, Russian Federation
b Higher School of Economics, Moscow, Russian Federation
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DOI: https://doi.org/10.26516/1997-7670.2021.37.77
Abstract: We prove new results about the inclusion of distributions of trigonometric polynomials in Gaussian random variables to Nikolskii–Besov classes. In addition, we estimate the total variance distances between distributions of trigonometric polynomials via the $L^q$-distances between the polynomials themselves.
Keywords: Nikolskii–-Besov class, Gaussian measure, distribution of a trigonometric polynomial.
Funding agency Grant number
Russian Science Foundation 17-11-01058
This research is supported by the Russian Science Foundation Grant 17-11-01058 (at Lomonosov Moscow State University).
Received: 05.06.2021
Bibliographic databases:
Document Type: Article
UDC: 519.2
MSC: 60E05, 60E015, 28C20, 60F99
Language: English
Citation: G. I. Zelenov, “On distributions of trigonometric polynomials in Gaussian random variables”, Bulletin of Irkutsk State University. Series Mathematics, 37 (2021), 77–92
Citation in format AMSBIB
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\by G.~I.~Zelenov
\paper On distributions of trigonometric polynomials in Gaussian random variables
\jour Bulletin of Irkutsk State University. Series Mathematics
\yr 2021
\vol 37
\pages 77--92
\mathnet{http://mi.mathnet.ru/iigum461}
\crossref{https://doi.org/10.26516/1997-7670.2021.37.77}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000707769800006}
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