
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 complexvalued 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 FourierPlancherel 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