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.

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

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