Real Analysis Exchange

Distribution of Polynomials in Many Variables and Nikolskii-Besov Spaces

Vladimir I. Bogachev

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Abstract

We discuss recent results and open problems connected with distributions of polynomials in many or infinitely many variables on spaces with Gaussian measures and Nikolskii--Besov spaces of fractional smoothness related to such distributions.

Article information

Source
Real Anal. Exchange, Volume 44, Number 1 (2019), 49-64.

Dates
First available in Project Euclid: 27 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.rae/1561622431

Digital Object Identifier
doi:10.14321/realanalexch.44.1.0049

Mathematical Reviews number (MathSciNet)
MR3951333

Zentralblatt MATH identifier
07088962

Subjects
Primary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 46E39: Sobolev (and similar kinds of) spaces of functions of discrete variables
Secondary: 46G25: (Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60] 60H07: Stochastic calculus of variations and the Malliavin calculus

Keywords
Nikolskii-Besov spaces distributions of polynomials Gaussian measure

Citation

Bogachev, Vladimir I. Distribution of Polynomials in Many Variables and Nikolskii-Besov Spaces. Real Anal. Exchange 44 (2019), no. 1, 49--64. doi:10.14321/realanalexch.44.1.0049. https://projecteuclid.org/euclid.rae/1561622431


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