It is proved that the Poisson measure is a spectral measure of some family of commuting selfadjoint operators acting on a space constructed from some generalization of the moment problem.
Yu. M. Berezansky, Poisson measure as a spectral measure of a family of commuting selfadjoint operators, connected with some moment problem, Methods Funct. Anal. Topology 22
(2016), no. 4, 311-329.
BibTex
@article {MFAT912,
AUTHOR = {Berezansky, Yu. M.},
TITLE = {Poisson measure as a spectral measure of a family of commuting selfadjoint operators, connected with some moment problem},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {22},
YEAR = {2016},
NUMBER = {4},
PAGES = {311-329},
ISSN = {1029-3531},
MRNUMBER = {MR3591083},
ZBLNUMBER = {06742114},
URL = {http://mfat.imath.kiev.ua/article/?id=912},
}
References
S. Albeverio, Yu. G. Kondratiev, and M. Rockner, Analysis and geometry on configuration spaces, J. Funct. Anal. 154 (1998), no. 2, 444-500. MathSciNetCrossRef
Yu. M. Berezansky, Spectral approach to white noise analysis, Dynamics of complex and irregular systems (Bielefeld, 1991), World Sci. Publ., River Edge, NJ, 1993, pp. 131-140. MathSciNet
Yu. M. Berezansky, Commutative Jacobi fields in Fock space, Integral Equations Operator Theory 30 (1998), no. 2, 163-190. MathSciNetCrossRef
Yu. M. Berezansky, Poisson measure as the spectral measure of Jacobi field, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 3 (2000), no. 1, 121-139. MathSciNetCrossRef
Yu. M. Berezansky, The generalized moment problem associated with correlation measures, Funct. Anal. Appl. 37 (2003), no. 4, 311-315. MathSciNetCrossRef
Yu. M. Berezansky and Y. G. Kondratiev, Spectral methods in infinite-dimensional analysis. Vol. 1, Kluwer Academic Publishers, Dordrecht, 1995. MathSciNetCrossRef
Yu. M. Berezansky, V. O. Livinsky, and E. W. Lytvynov, A generalization of Gaussian white noise analysis, Methods Funct. Anal. Topology 1 (1995), no. 1, 28-55. MathSciNet
Yu. M. Berezansky and D. A. Mierzejewski, The investigation of a generalized moment problem associated with correlation measures, Methods Funct. Anal. Topology 13 (2007), no. 2, 124-151. MathSciNet
Yu. M. Berezansky and V. A. Tesko, The investigation of Bogoliubov functionals by operator methods of moment problem, Methods Funct. Anal. Topology 22 (2016), no. 1, 1-47.
D. L. Finkelshtein, Stochastic dynamics of continuous systems, Ph.D. thesis, Institute of Mathematics of NAS of Ukraine, Kyiv, 2014.
Yoshifusa Ito and Izumi Kubo, Calculus on Gaussian and Poisson white noises, Nagoya Math. J. 111 (1988), 41-84. MathSciNet
Yuri G. Kondratiev and Tobias Kuna, Harmonic analysis on configuration space. I. General theory, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5 (2002), no. 2, 201-233. MathSciNetCrossRef
E. W. Lytvynov, Multiple Wiener integrals and non-Gaussian white noises: a Jacobi field approach, Methods Funct. Anal. Topology 1 (1995), no. 1, 61-85. MathSciNet
Eugene Lytvynov, The projection spectral theorem and Jacobi fields, Methods Funct. Anal. Topology 21 (2015), no. 2, 188-198. MathSciNet
M. J. Oliveira, Configuration space analysis and Poissonian white noise analysis, Ph.D. thesis, University of Lisbon, Lisbon, 2002.
K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, No. 3, Academic Press, Inc., New York-London, 1967. MathSciNet
