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Sbornik: Mathematics, 2010, Volume 201, Issue 10, Pages 1461–1493
DOI: https://doi.org/10.1070/SM2010v201n10ABEH004118
(Mi sm7571)
 

This article is cited in 1 scientific paper (total in 1 paper)

Model representations for systems of selfadjoint operators satisfying commutation relations

V. A. Zolotarevab

a V. N. Karazin Kharkiv National University
b B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
References:
Abstract: Model representations are constructed for a system {Bk}n1 of bounded linear selfadjoint operators in a Hilbert space H such that
[Bk,Bs]=i2φRk,sφ,σkφBsσsφBk=R+k,sφ,σkφφσsσsφφσk=2iRk,s,1k,sn,
where φ is a linear operator from H into a Hilbert space E and {σk,R±k,s}n1 are some selfadjoint operators in E. A realization of these models in function spaces on a Riemann surface is found and a full set of invariants for {Bk}n1 is described.
Bibliography: 11 titles.
Keywords: systems of selfadjoint operators, commutation relations, model representations.
Received: 29.04.2009 and 19.04.2010
Bibliographic databases:
Document Type: Article
UDC: 517.983.248
MSC: 47B15, 47A45, 47A48
Language: English
Original paper language: Russian
Citation: V. A. Zolotarev, “Model representations for systems of selfadjoint operators satisfying commutation relations”, Sb. Math., 201:10 (2010), 1461–1493
Citation in format AMSBIB
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\by V.~A.~Zolotarev
\paper Model representations for systems of selfadjoint operators satisfying commutation relations
\jour Sb. Math.
\yr 2010
\vol 201
\issue 10
\pages 1461--1493
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\crossref{https://doi.org/10.1070/SM2010v201n10ABEH004118}
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Linking options:
  • https://www.mathnet.ru/eng/sm7571
  • https://doi.org/10.1070/SM2010v201n10ABEH004118
  • https://www.mathnet.ru/eng/sm/v201/i10/p59
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
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    Abstract page:639
    Russian version PDF:196
    English version PDF:14
    References:63
    First page:20
     
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