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Analog of heat equation for gaussian measure of a ball in Hilberrt space

Authors:

Gyula Pap

Affiliation:

1. Department of Mathematics, University of Debrecen, Pf. 12, H-4010, Debrecen, Hungary

Abstract:

_a,T is a Gaussian measure on a Hilbert space with meana and covariance operatorT, andr is a fixed positive number, then the functiong(a,T)=_a,T{ Verbar

r} satisfies the equation

$frac{partial }{{partial T}}g(a,T) = frac{1}{2}frac{{partial ^2 }}{{partial a^2 }}g(a,T)$

Keywords:	Gaussian measure Hilbert space
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