|
This article is cited in 1 scientific paper (total in 1 paper)
On the boundary of the group of transformations leaving a measure quasi-invariant
Yu. A. Neretinabc
a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow
c University of Vienna
Abstract:
Let $A$ be a Lebesgue measure space. We interpret measures on $A\times A\times \mathbb R^\times$ as ‘maps’ from $A$ to $A$, which ‘spread’ $A$ along itself; their Radon-Nikodym derivatives are also spread. We discuss the basic properties of the semigroup of such maps and the action of this semigroup on the spaces $L^p(A)$.
Bibliography: 26 titles.
Keywords:
Lebesgue space, Markov operator, polymorphism, characteristic function, spaces $L^p$.
DOI:
https://doi.org/10.4213/sm8086
 Full text:
PDF file (798 kB)
References:
PDF file
HTML file
English version:
Sbornik: Mathematics, 2013, 204:8, 1161–1194
Bibliographic databases:
     
UDC:
517.518.112+512.583+517.983.23
MSC: Primary 22F10, 28A35; Secondary 28A33
Received: 17.11.2011 and 04.02.2013
Citation:
Yu. A. Neretin, “On the boundary of the group of transformations leaving a measure quasi-invariant”, Mat. Sb., 204:8 (2013), 83–116; Sb. Math., 204:8 (2013), 1161–1194
Citation in format AMSBIB
\Bibitem{Ner13}
\by Yu.~A.~Neretin
\paper On the boundary of the group of transformations leaving a~measure quasi-invariant
\jour Mat. Sb.
\yr 2013
\vol 204
\issue 8
\pages 83--116
\mathnet{http://mi.mathnet.ru/msb8086}
\crossref{https://doi.org/10.4213/sm8086}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3135689}
\zmath{https://zbmath.org/?q=an:06231592}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2013SbMat.204.1161N}
\elib{http://elibrary.ru/item.asp?id=20359269}
\transl
\jour Sb. Math.
\yr 2013
\vol 204
\issue 8
\pages 1161--1194
\crossref{https://doi.org/10.1070/SM2013v204n08ABEH004335}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000325549200005}
\elib{http://elibrary.ru/item.asp?id=21894697}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84888329107}
Linking options:
http://mi.mathnet.ru/eng/msb8086https://doi.org/10.4213/sm8086 http://mi.mathnet.ru/eng/msb/v204/i8/p83
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
Yu. A. Neretin, “Bi-invariant functions on the group of transformations leaving a measure quasi-invariant”, Sb. Math., 205:9 (2014), 1357–1372
|
| Number of views: |
| This page: | 279 | | Full text: | 63 | | References: | 52 | | First page: | 14 |
|
Terms of Use