Accession Number:
AD0431812
Title:
ON SPECTRAL REPRESENTATION FOR SELFADJOINT OPERATORS. EXPANSION IN GENERALIZED EIGENELEMENTS,
Descriptive Note:
Corporate Author:
KANSAS UNIV LAWRENCE
Personal Author(s):
Report Date:
1964-02-01
Pagination or Media Count:
41.0
Abstract:
A supplement to the theory of spectral representation for selfadjoint operators in a separable Hilbert space is presented. If m is a spectral measure for the selfadjoint operator A in a Hilbert space, then the classical theory of spectral representation sets up an isometric isomorphism mapping onto a suitable space of vector-valued functions on the real line. Various results in the classical theory hold m-almost everywhere, but the exceptional sets and the relations between them were not specified. A precise description of the exceptional sets is given, the consequences of this description will be useful for questions of expansion in generalized eigenelements of A. Author