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

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE