Accession Number : AD0756505

Title :   Integrals and Transforms in Function Space.

Descriptive Note : Final rept. 1 Jun 65-31 Aug 72,

Corporate Author : VIRGINIA UNIV CHARLOTTESVILLE

Personal Author(s) : McShane,E. J.

Report Date : 1973

Pagination or Media Count : 11

Abstract : A unified theory that includes ordinary calculus, theory of differential equations and theory of stochastic differential equations has been developed. Problems relating to classifying probability space were studied. Necessary and sufficient conditions were found for the operator equation BX-XA=Q, where B, A are self-adjoint operators in the space, beta(H), of bounded operators on a complex Hilbert space, Q belongs to beta(H), to have a solution in beta (H). Research on resonance problems focused on the question of the meaning, interpretation, and approximation of resonances (i.e., poles of a continued resolvent on S-matrix.) Gaussian processes, especially such processes in which the time parameter was in Euclidean n-space were studied. (Author)

Descriptors :   (*DIFFERENTIAL EQUATIONS, THEORY), INTEGRALS, OPERATORS(MATHEMATICS), STOCHASTIC PROCESSES, ANALYTIC FUNCTIONS, S MATRIX, POTENTIAL SCATTERING, RESONANCE, BIBLIOGRAPHIES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE