Accession Number : AD0431812


Title :   ON SPECTRAL REPRESENTATION FOR SELFADJOINT OPERATORS. EXPANSION IN GENERALIZED EIGENELEMENTS,


Corporate Author : KANSAS UNIV LAWRENCE


Personal Author(s) : Gerlach,Eberhard


Report Date : Feb 1964


Pagination or Media Count : 41


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)


Descriptors :   *ALGEBRAIC TOPOLOGY , FUNCTIONAL ANALYSIS , CONFORMAL MAPPING , RINGS , OPERATORS(MATHEMATICS) , TRANSFORMATIONS(MATHEMATICS) , INTEGRALS


Distribution Statement : APPROVED FOR PUBLIC RELEASE