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Russian Mathematical Surveys, 2016, Volume 71, Issue 4, Pages 703–749
DOI: https://doi.org/10.1070/RM9721 (Mi rm9721) 		 
This article is cited in 22 scientific papers (total in 23 papers)

Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures

V. I. Bogachev

National Research University "Higher School of Economics"
English version PDF (819 kB) Citations (23) Russian version article
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DOI: https://doi.org/10.1070/RM9721
Abstract: This paper provides a survey of recent investigations connected with distributions of polynomials on multi- and infinite-dimensional spaces with measures. The most important results on estimates (independent of the number of variables) for distribution functions and integral norms and also on convergence of the distributions of polynomials in variation and in the Kantorovich metric are presented. Interesting open problems in this area at the junction of the theory of functions, probability theory, and measure theory are discussed.
Bibliography: 131 titles.
Keywords: polynomials, distribution function, measurable polynomials, Gaussian measure, convex measure, logarithmically concave measure, convergence in variation, Kantorovich metric.
Funding agency Grant number
Russian Science Foundation 14-11-00196
This research was supported by grant no. 14-11-00196 from the Russian Science Foundation (at~Moscow State University).
Received: 09.05.2016
Bibliographic databases:
Document Type: Article
UDC: 519.2
MSC: Primary 28C20, 46G12, 46G25; Secondary 60B10, 60B11, 60E05
Language: English
Original paper language: Russian
Citation: V. I. Bogachev, “Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures”, Russian Math. Surveys, 71:4 (2016), 703–749
Citation in format AMSBIB
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\paper Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures
\jour Russian Math. Surveys
\yr 2016
\vol 71
\issue 4
\pages 703--749
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    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:925
    Russian version PDF:286
    English version PDF:34
    References:114
    First page:80
     
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