Accession Number : AD0662742

Title :   ORTHOGONALLY SCATTERED MEASURES.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Masani,P.

Report Date : AUG 1967

Pagination or Media Count : 93

Abstract : The report gives a coherent account of countably additive orthogonally scattered measures with values in a Hilbert space, and of the integration of complex-valued functions with respect to such measures. Some lacunae in the theory are cleared up. It is shown how the use of the concept of a basic orthogonally scattered measure in problems amenable to Hilbert space methods yields a unified treatment of the continuous and discrete aspects of such problems. The Fourier-Plancherel transformation over locally compact abelian groups is treated from this standpoint, and its bearing on the continuous eigenfunction expansions encountered in scattering theory is indicated. (Author)

Descriptors :   (*MEASURE THEORY, HILBERT SPACE), BANACH SPACE, STOCHASTIC PROCESSES, GROUPS(MATHEMATICS), FUNCTIONS(MATHEMATICS), BOUNDARY VALUE PROBLEMS, INTEGRAL TRANSFORMS, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE