Journal article
Extensions of positive definite integral kernels on the Heisenberg group
Journal of Functional Analysis, Vol.92(2), pp.474-508
1990
DOI: 10.1016/0022-1236(90)90060-X
Abstract
We consider positive definite extensions of functions and distributions which are defined on a cylindrical neighborhood (and positive definite) in the Heisenberg group. When rotational invariance is assumed, we show existence of p.d. extensions. We also give formulas (of the classical Bochner type) for all such extensions. They are expanded in terms of an integral transform associated to the sub-Laplacian. We further show that the p.d. extension problem is closely related to the theory of extensions of hermitian infinitesimal representations in the sense considered earlier by Powers and Fuglede. These are extensions to integrable representations in generally larger (so-called dilation ) Hilbert spaces.
Details
- Title: Subtitle
- Extensions of positive definite integral kernels on the Heisenberg group
- Creators
- Palle E.T Jorgensen
- Resource Type
- Journal article
- Publication Details
- Journal of Functional Analysis, Vol.92(2), pp.474-508
- DOI
- 10.1016/0022-1236(90)90060-X
- ISSN
- 1096-0783
- eISSN
- 1096-0783
- Language
- English
- Date published
- 1990
- Academic Unit
- Mathematics
- Record Identifier
- 9983986093002771
Metrics
16 Record Views