Abstract:
The properties of the integral transformation carrying boson Fock space into the L2 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.
Citation:
Yu. A. Neretin, “On the correspondence between boson Fock space and the L2 space with respect to Poisson measure”, Sb. Math., 188:11 (1997), 1587–1616
\Bibitem{Ner97}
\by Yu.~A.~Neretin
\paper On the correspondence between boson Fock space and the~$L^2$ space with respect to Poisson measure
\jour Sb. Math.
\yr 1997
\vol 188
\issue 11
\pages 1587--1616
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Linking options:
https://www.mathnet.ru/eng/sm275
https://doi.org/10.1070/sm1997v188n11ABEH000275
https://www.mathnet.ru/eng/sm/v188/i11/p19
This publication is cited in the following 10 articles:
V. V. Ryzhikov, “Weakly homoclinic groups of ergodic actions”, Trans. Moscow Math. Soc., 80 (2019), 83–94
V. V. Ryzhikov, “Weak Closure of Infinite Actions of Rank 1, Joinings, and Spectrum”, Math. Notes, 106:6 (2019), 957–965
I. V. Klimov, V. V. Ryzhikov, “Minimal Self-Joinings of Infinite Mixing Actions of Rank 1”, Math. Notes, 102:6 (2017), 787–791
V. V. Ryzhikov, J.-P. Thouvenot, “On the Centralizer of an Infinite Mixing Rank-One Transformation”, Funct. Anal. Appl., 49:3 (2015), 230–233
Pugachev, OV, “Quasi-invariance of Poisson distributions with respect to transformations of configurations”, Doklady Mathematics, 77:3 (2008), 420
Yu. A. Neretin, “Spreading maps (polymorphisms), symmetries of poisson processes, and matching summation”, J Math Sci, 126:2 (2005), 1077
Neretin, YA, “Structures of boson and fermion Fock spaces in the space of symmetric functions”, Acta Applicandae Mathematicae, 81:1 (2004), 233
A. M. Vershik, N. V. Tsilevich, “Fock factorizations, and decompositions of the L2 spaces over general Lévy processes”, Russian Math. Surveys, 58:3 (2003), 427–472
Yu. A. Neretin, “Spreading maps (polymorphisms), symmetries of Poisson processes, and matching summation”, J. Math. Sci. (N. Y.), 126:2 (2005), 1077–1094
Yu. A. Neretin, “Supercomplete Bases in the Space of Symmetric Functions”, Funct. Anal. Appl., 32:1 (1998), 10–22
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