ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2020. Vol. 31

Fractional Smoothness of Distributions of Trigonometric Polynomials on a Space with a Gaussian Measure

G. I. Zelenov

In this paper we study properties of images of a gaussian measure under trigonometric polynomials of a fixed degree, defined on finite-dimensional space with fixed number of dimensions. We prove that the images of the n-dimensional Gaussian measure under trigonometric polynomials have densities from the Nikolskii – Besov class of fractional parameter. This property of images of a gaussian measure is used for estimating the total variation distance between such images via the Fortet – Mourier distance. We also generalize these results to the case of k-dimensional mappings whose components are trigonometric polynomials.

About the Authors

Georgii Zelenov, PhD (Phys.–Math.), Junior Research Fellow, Moscow State University, 1, Leninskie Gory, Moscow, 119991, Russian Federation; Assoc. Prof., National Research University Higher School of Economics, 20, Myasnitskaya ulitsa, Moscow, 101000, Russian Federation, e-mail: zelenovyur@gmail.com

For citation

Zelenov G.I. Fractional Smoothness of Distributions of Trigonometric Polynomials on a Space with a Gaussian Measure. The Bulletin of Irkutsk State University. Series Mathematics, 2020, vol. 31, pp. 78-95. (in Russian) https://doi.org/10.26516/1997-7670.2020.31.78

Nikolskii – Besov class, Gaussian measure, distribution of a trigonometric polynomial
60E05, 60E015; 28C20, 60F99

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