On the relations between Poissonian white noise analysis and harmonic analysis on configuration spaces

Journal of Functional Analysis

Volumn 213, Issue 1, 2004, Pages 1-30

  Kondratiev, Yuri G ^a,b   Kuna, Tobias ^a   Oliveira, Maria Joã ^a,b,c,d  

^a BIELEFELD UNIVERSITY   (Germany)

^b INSTITUTE OF MATHEMATICS   (Ukraine)

^c UNIVERSIDADE ABERTA   (Portugal)

^d UNIVERSITY OF LISBON   (Portugal)

Author keywords

Chaos decomposition; Configuration spaces; Continuous system; Correlation function; Gibbs measure; Poisson measure

Indexed keywords

EID: 3042771620     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2004.04.010     Document Type: Article

References (25)

1. Berezansky Yu.M. Kondratiev Yu.G. Spectral Methods in Infinite-dimensional Analysis 1988 Naukova Dumka Kiev (in Russian) (English translation, Kluwer Academic Publishers, Dordrecht, 1995)
2. Bogoliubov N.N. Problems of a Dynamical Theory in Statistical Physics 1946 Gostekhisdat Moscow (in Russian) (English translation, in: J. de Boer, G.E. Uhlenbeck (Eds.), Studies in Statistical Mechanics, Vol. 1, North-Holland, Amsterdam, 1962, pp. 1-118)
3. Daley D.J. Vere-Jones D. An Introduction to the Theory of Point Processes 1988 Springer New York, Berlin, Heidelberg
4. Fichtner K.-H. Freudenberg W. Characterization of states of infinite Boson systems I, On the construction of states of Boson systems Commun. Math. Phys. 137 1991 315-357
5. Gerasimenko V.I. Malyshev P.V. Petrina D.Ya. Mathematical Foundations of Classical Statistical Mechanics: Continuous Systems in: Advanced Studies in Contemporary Mathematics Vol. 6 1989 Gordon and Breach Science Publishers London, New York
6. T. Hida, N. Ikeda, Analysis on Hilbert space with reproducing kernel arising from multiple Wiener integral, in: Proceedings of the 5th Berkeley Symposium on Mathematical and Statistical Probability, Vol. 2, 1967, pp. 117-143.
7. Holden H. Øksendal B. A white noise approach to stochastic differential equations driven by Wiener and Poisson processes In: Grosser M. (Ed.) et al. Nonlinear Theory of Generalized Functions 1999 293-313 Chapman & Hall/CRC London/Boca Raton, FL
8. Ito Y. Generalized Poisson functionals Probab. Theory Related Fields 77 1988 1-28
9. 1Ito Y. Kubo I. Calculus on Gaussian and Poisson white noises Nagoya Math. J. 111 1988 41-84
10. Kondratiev Yu. G. Kuna T. Harmonic analysis on configuration space I, General theory Infinite Dimensional Anal. Quantum Probab. Related Topics 5 2 2002 201-233
11. Yu.G. Kondratiev, T. Kuna, Harmonic analysis on configuration space II, Bogoliubov functional and equilibrium states, 2004, in preparation.
12. Kondratiev Yu.G. Kuna T. Oliveira M.J. Analytic aspects of Poissonian white noise analysis Methods Funct. Anal. Topol. 8 4 2002 15-48
13. Yu.G. Kondratiev, T. Kuna, M.J. Oliveira, Non-equilibrium stochastic dynamics of continuous systems and Bogoliubov functionals, 2004, in preparation.
14. Yu.G. Kondratiev, M.J. Oliveira, Invariant measures for Glauber dynamics of continuous systems, BiBoS Preprint no. 03-10-130, University of Bielefeld, October 2003; Madeira Preprint no. 83/03, University of Madeira, August 2003; arXiv:math-ph/0307050, July, 2003.
15. Kondratiev Yu.G. Silva J.L. Streit L. Generalized Appell systems Methods Funct. Anal. Topol. 3 2 1997 28-61
16. Kondratiev Yu.G. Streit L. Westerkamp W. Yan J. Generalized functions in infinite dimensional analysis Hiroshima Math. J. 28 2 1998 213-260
17. T. Kuna, Studies in Configuration Space Analysis and Applications, Ph.D. Thesis, Bonner Mathematische Schriften No. 324, University of Bonn, 1999.
18. Lenard A. Correlation functions and the uniqueness of the state in classical statistical mechanics Commun. Math. Phys. 30 1973 35-44
19. Lenard A. States of classical statistical mechanical systems of infinitely many particles I Arch. Rational Mech. Anal. 59 1975 219-239
20. Lenard A. States of classical statistical mechanical systems of infinitely many particles II Arch. Rational Mech. Anal. 59 1975 241-256
21. M.J. Oliveira, Configuration space analysis and Poissonian white noise analysis, Ph.D. Thesis, Faculty of Sciences, University of Lisbon, 2002.
22. Ruelle D. Statistical Mechanics, Rigorous Results 1969 Benjamin New York, Amsterdam
23. Ruelle D. Superstable interactions in classical statistical mechanics Commun. Math. Phys. 18 1970 127-159
24. Skorohod A.V. Integration in Hilbert Space 1974 Springer Berlin, Heidelberg, New York
25. Surgailis D. On multiple Poisson stochastic integrals and associated Markov semigroups Probab. Math. Statist. 3 1984 217-239