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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 81, 2009 - Issue 3-4: Stochastic Analysis
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Original Articles

Analytical functionals and application to Poissonian and harmonic analysis

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Pages 219-240 | Received 14 May 2008, Accepted 28 Jul 2008, Published online: 23 Jul 2009

References

  • Aubin , T. 1982 . Nonlinear Analysis on Manifolds, Monge–Ampère Equation , Berlin Heigelberg New York : Springer .
  • Berezansky , Yu. M. and Kondratiev , Yu. Spectral Methods in Infinite-Dimensional Analysis , Naukova Dumka . Kiev, 1988 (in Russian). English translation, Kluwer Academic Publishers, Dordrecht, 1995
  • Bogoliubov , N.N. 1962 . Problems of dynamical theory in statistical physics , Gostekhisdat, Moscow, 1946 (in Russian) Edited by: de Boer , J. and Uhlenbeck , G.E. Vol. 1 , 1 – 118 . Amsterdam : North-Holland . English translation, in Studies in Statistical Mechanics
  • Carter , D.S. and Prenter , P.M. 1972 . Exponential spaces and counting processes . Z. Wahrscheinlichkeitstheorie Verw. Geb. , 21 : 1 – 19 .
  • Chaari , S. and Ouerdiane , H. 2006 . White noise analysis in the Poisson space . Afr. Diaspora J. Math. , 4 ( 2 ) : 12 – 24 .
  • Gannoun , R. , Hchaichi , R. , Ouerdiane , H. and Rezgui , A. 2000 . Un théorème de dualité entre espaces de fonctions holomorphes à croissance exponentielle . J. Funct. Anal. , 171 ( 1 ) : 1 – 14 .
  • Gelfand , I.M. and Vilenkin , N.Ya. 1968 . Generalized Functions , Vol. IV , New York and London : Academic Press .
  • Guichardet , A. 1972 . Symmetric Hilbert Spaces and Related Topics , Lecture Notes in Mathematics Vol. 261 , Berlin/Heidelberg/New York : Springer Verlag .
  • Hida , T. 1975 . Analysis of Brownian Functionals , Carleton Mathematical Lecture Notes Vol. 13 , Ottawa : Carleton University .
  • Hida , T. 1980 . Brownian Motion , New York : Springer Verlag .
  • Ito , Y. 1988 . Generalized Poisson functionals . Probab. Theory Related Fields , 77 : 1 – 28 .
  • Ito , Y. and Kubo , I. 1988 . Calculus on Gaussian and Poisson white noises . Nagoya Math. J. , 111 : 41 – 64 .
  • Kondratiev , Yu. G. and Kuna , T. 2002 . Harmonic analysis on configuration space I, general theory . Infin. Dimens. Anal. Quantum Probab. Relat. Top. , 5 ( 2 ) : 201 – 233 .
  • Kondratiev , Yu. G. , Streit , L. , Westerkamp , W. and Yan , J. 1998 . Generalized functions in infinite dimensional analysis . Hiroshima Math. J. , 28 ( 2 ) : 213 – 260 .
  • Kondratiev , Yu. G. , Kuna , T. and Oliveira , M.J. 2004 . On the relations between Poissonian white noise analysis and harmonic analysis on configuration space . J. Funct. Anal. , 213 : 1 – 30 .
  • Kubo , I. and Takenaka , S. 1980 . Calculus on Gaussian white noise, I . Proc. Japan Acad. Ser. A Math. Sci. , 56 ( 8 ) : 376 – 380 .
  • T. Kuna, Studies in configuration space analysis and applications, PhD thesis, Bonner Mathematishe Schriften Nr. 324, University of Bonn, 1999
  • Lenard , A. 1973 . Coerrelation functions and the uniqueness of the state in classical statistical mechanics . Commun. Math. Phys. , 30 : 35 – 44 .
  • Shimoura , H. 1994 . Poisson measure on the configuration space and unitary representation of the groupe of diffeomorphisms . J. Math. Kyoto. , 34 : 599 – 614 .
  • Vershik , A.M. , Gelfand , I.M. and Graev , M.I. 1975 . Representation of group of diffeomorphisms . Uspekhi Mat. Nauk , 30 : 1 – 50 .

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