Geodesic
On distributions of trigonometric polynomials in Gaussian random variables
The Bulletin of Irkutsk State University. Series Mathematics, Tome 37 (2021), pp. 77-92

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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: Gaussian measure, distribution of a trigonometric polynomial.
Mots-clés : Nikolskii–-Besov class 
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     author = {G. I. Zelenov},
     title = {On distributions of trigonometric polynomials in {Gaussian} random variables},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {77--92},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2021_37_a5/}
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G. I. Zelenov. On distributions of trigonometric polynomials in Gaussian random variables. The Bulletin of Irkutsk State University. Series Mathematics, Tome 37 (2021), pp. 77-92. http://geodesic.mathdoc.fr/item/IIGUM_2021_37_a5/