Journal article
Extension of positive definite functions
Journal of mathematical analysis and applications, Vol.422(1), pp.712-740
02/01/2015
DOI: 10.1016/j.jmaa.2014.09.002
Abstract
Let Ω⊂Rn be an open, connected subset of Rn, and let F:Ω−Ω→C, where Ω−Ω={x−y:x,y∈Ω}, 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.
Details
- Title: Subtitle
- Extension of positive definite functions
- Creators
- Palle E.T Jorgensen - Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA-52242, USARobert Niedzialomski - Department of Mathematics and Statistics, The University of Tennessee at Martin, 424 Humanities Building, Martin, TN-38238, USA
- Resource Type
- Journal article
- Publication Details
- Journal of mathematical analysis and applications, Vol.422(1), pp.712-740
- DOI
- 10.1016/j.jmaa.2014.09.002
- ISSN
- 0022-247X
- eISSN
- 1096-0813
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 02/01/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9983985866902771
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