On Distributions of Trigonometric Polynomials in Gaussian Random Variables

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