ORTHOGONALLY SCATTERED MEASURES.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1967
- Accession Number
- AD0662742
Entities
People
- P. Masani
Organizations
- University of Wisconsin–Madison