Heat kernel analysis and Cameron-Martin subgroup for infinite dimensional groups

Journal of Functional Analysis

Volumn 171, Issue 1, 2000, Pages 192-232

  Gordina, Maria ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

Heat kernel measure; Holomorphic function; Infinite dimensional group; Infinite dimensional Lie algebra; Stochastic differential equation

Indexed keywords

EID: 0009928227     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1999.3505     Document Type: Article

References (16)

1. Bargmann V. On a Hilbert space of analytic functions and an associated integral transform, I. Comm. Pure Appl. Math. 24:1961;187-214.
2. Bargmann V. Remarks on a Hilbert space of analytic functions. Proc. Nat. Acad. Sci. U.S.A. 48:1962;199-204.
3. DaPrato G., Zabczyk J. Stochastic Equations in Infinite Dimensions. 1992;Cambridge Univ. Press, Cambridge.
4. Driver B. On the Kakutani-Itô-Segal-Gross and Segal-Bargmann-Hall isomorphisms. J. Funct. Anal. 133:1995;69-128.
5. Driver B., Gross L. Hilbert spaces of holomorphic functions on complex Lie groups. Elworthy K. D., Kusuoka S., Shigekawa I. Proceedings of the 1994 Taniguchi International Workshop. 1997;World Scientific, Singapore/New Jersey/London/Hong Kong.
6. Dynkin E. B. Calculation of the coefficients in the Campbell-Hausdorff formula. Dokl. Akad. Nauk USSR (N.S.). 57:1947;323-326.
7. M. Gordina, Holomorphic functions and the heat kernel measure on an infinite dimensional complex orthogonal groups, Potential Anal, to appear.
8. Gross L., Malliavin P. Hall's transform and the Segal-Bargmann map. Fukushima M., Ikeda N., Kunita H., Watanabe S. Itô's Stochastic Calculus and Probability Theory. 1996;Springer-Verlag, New York/Berlin.
9. Hall B. The Segal-Bargmann "coherent state" transform for compact Lie groups. J. Funct. Anal. 122:1994;103-151.
10. B. Hall, and, A. Sengupta, The Segal-Bargmann transform for paths in a compact groups, in preparation, 1997.
11. Hijab O. Hermite functions on compact Lie groups, I. J. Funct. Anal. 125:1994;480-492.
12. Hijab O. Hermite functions on compact Lie groups, II. J. Funct. Anal. 133:1995;41-49.
13. Martin R. H. Jr. Nonlinear operators and differential equations in Banach spaces. Pure and Applied Mathematics. 1976;Wiley-Interscience, New York/London/Sydney.
14. Shigekawa I. Itô-Wiener expansions of holomorphic functions on the complex Wiener space. Mayer E. Stochastic Analysis. 1991;459-473 Academic Press, San Diego.
15. Sugita H. Properties of holomorphic Wiener functions - Skeleton, contraction, and local Taylor expansion. Probab. Theory Related Fields. 100:1994;117-130.
16. Sugita H. Regular version of holomorphic Wiener function. J. Math. Kyoto Univ. 34:1994;849-857.