The Segal-Bargmann transform for Lévy functionals

Journal of Functional Analysis

Volumn 168, Issue 1, 1999, Pages 46-83

  Lee, Yuh Jia ^a   Shih, Hsin Hung ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0342450892     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1999.3452     Document Type: Article

References (18)

1. J. L. Doob, "Stochastic Processes," Wiley, New York, 1953.
2. I. M. Gel'fand and N. Y. Vilenkin, "Generalized Functions," Vol. 4, Academic Press, New York, 1964.
3. L. Gross and P. Malliavin, Hall's transform and the Segal-Bargmann map, in "Itô's Stochastic Calculus and Probability Theory" (M. Fukushima et al., Eds.), Springer-Verlag, New York/Berlin, 1996.
4. T. Hida, "Analysis of Brownian Functionals," Carleton Mathematical Lecture Notes, Vol. 13, 1975.
5. T. Hida, H.-H. Kuo, J. Potthoff, and L. Streit, "White Noise: An Infinite Dimensional Calculus," Kluwer Academic, 1993.
6. K. Itô, Multiple Wiener integral, Jap. J. math. 22 (1952), 157-169.
7. K. Itô, On stochastic processes, Jap. J. Math. 18 (1942), 261-301.
8. K. Itô, Spectral type of shift transformations of differential process with stationary increments, Trans. Amer. Math. Soc. 81 (1956), 253-263.
9. Y. Itô, Generalized Poisson functionals, Probab. Theory Relat. Fields 77 (1988), 1-28.
10. I. Kubo and S. Takenaka, Calculus on Gaussian white noises, II, Proc. Japan Acad. Ser. A Math. Sci. 56 (1980), 411-416.
11. H.-H. Kuo, "White Noise Distribution Theory," CRC Press, Boca Raton, New York/ London/Tokyo, 1996.
12. Y.-J. Lee, Analytic version of test functionals, Fourier transform, and a characterization of measures in white noise calculus, J. Funct. Anal. 100 (1991), 359-380.
13. Yu. G. Kondratiev, J. L. Silva, L. Streit, and F. G. Us, Analysis on Poisson and Gamma spaces, Infinite Dimensional Anal. Quantum Probab. Relat. Topics 1 (1998), 91-117.
14. E. W. Lytvynov, A. L. Rebenko, and G. V. Shchepa'nuk, Wick calculus on spaces of generalized functions of compound Poisson white noise, Rep. Math. Phys. 39 (1997), 219-248.
15. N. Privault, Chaotic and variational calculus in discrete and continuous time for the Poisson process, Stochast. Stochast. Rep. 51, Nos. 1-2 (1994), 83-109.
16. N. Privault, A different quantum stochastic calculus for the Poisson process, Probab. Theroy Relat. Fields 105 (1996), 225-278.
17. N. Privault, A transfer principle from Wiener to Poisson space and application, J. Funct. Anal. 132 (1995), 335-360.
18. J. L. Silva, "Studies in Non-Gaussian Analysis," Ph.D. dissertation, University of Madeira, 1998.