Integrals and Transforms in Function Space.
Final rept. 1 Jun 65-31 Aug 72,
VIRGINIA UNIV CHARLOTTESVILLE
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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-XAQ, where B, A are self-adjoint operators in the space, betaH, of bounded operators on a complex Hilbert space, Q belongs to betaH, 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
- Statistics and Probability