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