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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
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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
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http://mi.mathnet.ru/eng/msb275https://doi.org/10.4213/sm275 http://mi.mathnet.ru/eng/msb/v188/i11/p19
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This publication is cited in the following articles:
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Yu. A. Neretin, “Supercomplete Bases in the Space of Symmetric Functions”, Funct. Anal. Appl., 32:1 (1998), 10–22
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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
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Neretin, YA, “Structures of boson and fermion Fock spaces in the space of symmetric functions”, Acta Applicandae Mathematicae, 81:1 (2004), 233
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Pugachev, OV, “Quasi-invariance of Poisson distributions with respect to transformations of configurations”, Doklady Mathematics, 77:3 (2008), 420
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V. V. Ryzhikov, J.-P. Thouvenot, “On the Centralizer of an Infinite Mixing Rank-One Transformation”, Funct. Anal. Appl., 49:3 (2015), 230–233
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I. V. Klimov, V. V. Ryzhikov, “Minimal Self-Joinings of Infinite Mixing Actions of Rank 1”, Math. Notes, 102:6 (2017), 787–791
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