INTEGRAL KERNEL OPERATORS ON REGULAR GENERALIZED WHITE NOISE FUNCTIONS

Abstract

Let (and ) be the space of regular test (and generalized, resp.) white noise functions. The integral kernel operators acting on and transformation groups of operators on are studied, and then every integral kernel operator acting on can be extended to continuous linear operator on . The existence and uniqueness of solutions of Cauchy problems associated with certain integral kernel operators with intial data in are investigated.