Open Access
October, 2015 Holomorphic functions and the Itô chaos
J. Math. Soc. Japan 67(4): 1449-1484 (October, 2015). DOI: 10.2969/jmsj/06741449


This paper is concerned with the characterization of spaces of square integrable holomorphic functions on a complex manifold, $G$, in terms of the derivatives of the function at a fixed point $o\in G$. The reproducing kernel properties of square integrable holomorphic functions are reviewed and a number of examples are given. These examples include square integrable holomorphic functions relative to Gaussian measures on complex Euclidean spaces along with their generalizations to heat kernel measures on complex Lie groups. These results are intimately related to the Itô's chaos expansion in stochastic analysis and to the Fock space description of free quantum fields in physics.


Download Citation

Bruce K. DRIVER. "Holomorphic functions and the Itô chaos." J. Math. Soc. Japan 67 (4) 1449 - 1484, October, 2015.


Published: October, 2015
First available in Project Euclid: 27 October 2015

zbMATH: 1336.32019
MathSciNet: MR3417503
Digital Object Identifier: 10.2969/jmsj/06741449

Primary: 32W30 , 60H10
Secondary: 35H20 , 43A15

Keywords: complex groups , Fock space , hypo-elliptic heat Kerenels , Itô chaos , Taylor map

Rights: Copyright © 2015 Mathematical Society of Japan

Vol.67 • No. 4 • October, 2015
Back to Top