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.

Georgii Zelenov, PhD (Phys.–Math.), Junior Research Fellow, Department of Mechanics and Mathematics, Moscow State University, 1, Leninskie Gory, Moscow, 119991, Russian Federation; Assoc. Prof., Faculty of Computer Science, National Research University Higher School of Economics, 20, Myasnitskaya ulitsa, Moscow, 101000, Russian Federation, email: zelenovyur@gmail.com

Zelenov G.I. On Distributions of Trigonometric Polynomials in Gaussian Random Variables. The Bulletin of Irkutsk State University. Series Mathematics, 2021, vol. 37, pp. 77-92. https://doi.org/10.26516/1997-7670.2021.37.77

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