Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6418123 | Journal of Mathematical Analysis and Applications | 2015 | 29 Pages |
Abstract
Let ΩâRn be an open, connected subset of Rn, and let F:ΩâΩâC, where ΩâΩ={xây:x,yâΩ}, be a continuous positive definite function. We give necessary and sufficient conditions for F to have an extension to a continuous positive definite function defined on the entire Euclidean space Rn. The conditions are formulated in terms of existence of a unitary representations of Rn whose generators extend a certain system of unbounded Hermitian operators defined on a Hilbert space associated to F. Different positive definite extensions correspond to different unitary representations.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Palle E.T. Jorgensen, Robert Niedzialomski,