ON SPECTRAL REPRESENTATION FOR SELFADJOINT OPERATORS. EXPANSION IN GENERALIZED EIGENELEMENTS,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1964
- Accession Number
- AD0431812
Entities
People
- Eberhard Gerlach
Organizations
- University of Kansas