ON INTEGRAL-REPRESENTATION OF THE CONTINUOUS O(N)-POSITIVE DEFINITE FUNCTIONS

Authors
BECKER MB
Citation
Mb. Becker, ON INTEGRAL-REPRESENTATION OF THE CONTINUOUS O(N)-POSITIVE DEFINITE FUNCTIONS, Integral equations and operator theory, 31(2), 1998, pp. 133-149
Citations number
15
Categorie Soggetti
Mathematics,Mathematics
Journal title
Integral equations and operator theory → ACNP
ISSN journal
0378620X
Volume
31
Issue
2
Year of publication
1998
Pages
133 - 149
Database
ISI
SICI code
0378-620X(1998)31:2<133:OIOTCO>2.0.ZU;2-K
Abstract
The aim of this paper is to study integral representation for continuo us O(n)-positive definite functions. Using the Krein method of directi ng functionals we prove the theorem about integral representation, giv e the criteria of uniqueness of this representation and description of all representations in the case of ununiqueness. On the basis of thes e results we solve analogous problems for continuous radial positive d efinite functions.