ON A DUAL PAIR OF SPACES OF SMOOTH AND GENERALIZED RANDOM-VARIABLES

A dual pair G and G* of smooth and generalized random variables, respectively, over the white noise probability space is studied. G is constructed by norms involving exponentials of the Ornstein-Uhlenbeck operator, G* is its dual. Sufficient criteria are proved for when a function on L(R) is the L-transform of an element in G or G*.