Bulletin of the Australian Mathematical Society

Table of Contents - December 2003 - Volume 68, Issue 03  

Research Article

Differential equations in spaces of Hilbert space valued distributions

Maxim Alshanskya1

a1 Ural State Technical University, Yekaterinburg, Russia, e-mail: mxa@mail.ur.ru

Abstract

A Gaussian measure is introduced on the space of Hilbert space valued tempered distributions. It is used to define a Hilbert space valued Q-Wiener process and a white noise process with a nuclear covariance operator Q. The proposed construction is used for solving operator-differential equations with additive noise with the operator coefficient generating an n-times integrated exponentially bounded semigroup.

(Received June 11 2003)