Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 1996; 33(3): 541-555

Printed September 1, 1996

Copyright © The Korean Mathematical Society.

Heat equation in white noise analysis

Jung-Soon Kim Lee

Southern University

Abstract

It is known that if $f$ is a bounded Lip-1 function on an abstract Wiener space with Gaussian measures $P_t$, then $u(t) = P_t f$ solves the heat equation $ {d \over{dt}}u(t) = {1\over2 }\D_G u(t)$ with initial condition $u(0) = f$ where $\D_G$ is the Gross' Laplacian. We show that if $\vp$ is in $\SS$, then $u(t) = P_t \vp$ is also in $\SS$ and satisfies ${ d\over{dt}} u(t) = {1\over 2}\D_G u(t)$ with $u(0) = f$.

Keywords: Gross Laplacian, Wiener measure, White noise space

MSC numbers: 46G25