Accession Number : AD0292915

Title :   LINEAR TRANSFORMATIONS OF A FUNCTIONAL INTEGRAL, II

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : SEIDMAN,THOMAS I.

Report Date : OCT 1962

Pagination or Media Count : 1

Abstract : It was proved in Seidman, T. I., Linear Transformations of a Functional Integral, I; Comm. Pure and Appl. Math., Vol. XII, No. 4 (1959), that the measure on the countable direct product of real lines wth identical normally distributed measures, transforms (with a specified RadonNikodym derivative) to an equivalent (mutually absolutely continuous) measure under li ear transformations of the form T = I + A with A a non-singular, Hilbert-Schmidt operator with finite trace (evaluated with respect to the canonical basis). We shall extend this result to transformations of the form T = U(I + A) where U is unitary and A non-singular and HilbertSchmidt but with no traceability condition imposed. (Author)

Descriptors :   *NUMERICAL INTEGRATION, *MEASURE THEORY, *TOPOLOGY, *TRANSFORMATIONS (MATHEMATICS)

Distribution Statement : APPROVED FOR PUBLIC RELEASE