Russian Mathematical Surveys
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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)
References:
PDF
HTML
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
Russian version:
Uspekhi Matematicheskikh Nauk, 2016, Volume 71, Issue 4(430), Pages 107–154
DOI: https://doi.org/10.4213/rm9721
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”, Uspekhi Mat. Nauk, 71:4(430) (2016), 107–154; Russian Math. Surveys, 71:4 (2016), 703–749
Citation in format AMSBIB
\Bibitem{Bog16}
\by V.~I.~Bogachev
\paper Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures
\jour Uspekhi Mat. Nauk
\yr 2016
\vol 71
\issue 4(430)
\pages 107--154
\mathnet{http://mi.mathnet.ru/rm9721}
\crossref{https://doi.org/10.4213/rm9721}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3588922}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2016RuMaS..71..703B}
\elib{https://elibrary.ru/item.asp?id=26604181}
\transl
\jour Russian Math. Surveys
\yr 2016
\vol 71
\issue 4
\pages 703--749
\crossref{https://doi.org/10.1070/RM9721}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000391301300002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84997335275}
Linking options:
  • https://www.mathnet.ru/eng/rm9721
  • https://doi.org/10.1070/RM9721
  • https://www.mathnet.ru/eng/rm/v71/i4/p107
    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:888
    Russian version PDF:273
    English version PDF:30
    References:110
    First page:80
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024