On distributions of trigonometric polynomials in Gaussian random variables

DOI10.26516/1997-7670.2021.37.77zbMath1476.60032OpenAlexW3201134987MaRDI QIDQ823959

Georgiĭ Il'ich Zelenov

Publication date: 14 December 2021

Published in: Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika (Search for Journal in Brave)

Full work available at URL: http://mathizv.isu.ru/en/article/file?id=1386

zbMATH Keywords

Gaussian measureNikolskii-Besov classdistribution of a trigonometric polynomial

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Limit theorems in probability theory (60F99)

Cites Work

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• Membership of distributions of polynomials in the Nikolskii-Besov class
• On distance in total variation between image measures
• Fractional smoothness of images of logarithmically concave measures under polynomials
• Convergence in total variation on Wiener chaos
• Fractional smoothness of distributions of trigonometric polynomials on a space with a Gaussian measure
• Distribution of polynomials in many variables and Nikolskii-Besov spaces
• Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures
• Fractional smoothness of distributions of polynomials and a fractional analog of the Hardy–Landau–Littlewood inequality
• Besov classes on finite and infinite dimensional spaces
• A new approach to Nikolskii-Besov classes
• Distributional and \(L^q\) norm inequalities for polynomials over convex bodies in \(\mathbb{R}^n\)

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