## A fundamental solution of the parabolic equation on Hilbert space |

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absolutely continuous B-continuity B-Lip 1 function Banach space bounded B-Lip bounded linear operator bounded measurable functions canonical normal distribution change of variables completion of H continuous functions continuous with respect converges in probability countably additive cylinder set measure D C(x denote differentiable with respect directions of H exists a constant f(x+h f(x+y family of measures family of operators finite dimensional projection Frechet differentiable function f functions on H fundamental solution Gauss measure given H with respect Hilbert space Hilbert-Schmidt class operator independent of f Lemma measurable function measurable norm measurable semi-norm measures rt(x,dy Mtf(x obtain operator norm operators on H orthonormal basis P B(x parabolic equation Pl(dy projection on H proof Proposition pt(dy QB(x qt(x,dy random variables real-valued rtf(x second order second Prechet derivative subset symmetric Hilbert-Schmidt class Theorem trace a(x trace class operators u.c.n.O in H uniformly bounded weak distribution Wiener space x,dy