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Mat. Sb., 1997, Volume 188, Number 11, Pages 19–50 (Mi msb275)  

This article is cited in 6 scientific papers (total in 6 papers)

On the correspondence between boson Fock space and the $L^2$ space with respect to Poisson measure

Yu. A. Neretin

Moscow State Institute of Electronics and Mathematics

Abstract: The properties of the integral transformation carrying boson Fock space into the $L^2$ space with respect to Poisson measure are investigated. An explicit formula is obtained for point configuration functions corresponding to Gaussian vectors of boson Fock space.

DOI: https://doi.org/10.4213/sm275

Full text: PDF file (406 kB)
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English version:
Sbornik: Mathematics, 1997, 188:11, 1587–1616

Bibliographic databases:

UDC: 519.46+517.4
MSC: Primary 47N50, 46N50; Secondary 47B38, 81R10, 81S05, 47B10, 32A30, 22E70
Received: 11.03.1997

Citation: Yu. A. Neretin, “On the correspondence between boson Fock space and the $L^2$ space with respect to Poisson measure”, Mat. Sb., 188:11 (1997), 19–50; Sb. Math., 188:11 (1997), 1587–1616

Citation in format AMSBIB
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    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:
    1. Yu. A. Neretin, “Supercomplete Bases in the Space of Symmetric Functions”, Funct. Anal. Appl., 32:1 (1998), 10–22  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. M. Vershik, N. V. Tsilevich, “Fock factorizations, and decompositions of the $L^2$ spaces over general Lévy processes”, Russian Math. Surveys, 58:3 (2003), 427–472  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Neretin, YA, “Structures of boson and fermion Fock spaces in the space of symmetric functions”, Acta Applicandae Mathematicae, 81:1 (2004), 233  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    4. Pugachev, OV, “Quasi-invariance of Poisson distributions with respect to transformations of configurations”, Doklady Mathematics, 77:3 (2008), 420  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    5. V. V. Ryzhikov, J.-P. Thouvenot, “On the Centralizer of an Infinite Mixing Rank-One Transformation”, Funct. Anal. Appl., 49:3 (2015), 230–233  mathnet  crossref  crossref  isi  elib
    6. I. V. Klimov, V. V. Ryzhikov, “Minimal Self-Joinings of Infinite Mixing Actions of Rank 1”, Math. Notes, 102:6 (2017), 787–791  mathnet  crossref  crossref  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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