POLYNOMIAL-APPROXIMATION FOR A CLASS OF PHYSICAL RANDOM-VARIABLES

In white noise theory on Hilbert spaces, it is known that maps which a re uniformly continuous around the origin in the S-topology constitute an important class of ''physical'' random variables. We prove that ra ndom variables having such a continuity property can be approximated i n the gaussian measure by polynomial random variables. The proof relie s on representing functions which are uniformly S-continuous around th e origin as the composition of a continuous map with a Hilbert-Schmidt operator.