Journal article
Reproducing Kernel Hilbert Space vs. Frame Estimates
Mathematics, Vol.3(3), pp.615-625
07/01/2015
DOI: 10.3390/math3030615
Abstract
We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are functions on some set $\Omega$. We then identify conditions on these functions which automatically give $\mathcal{H}$ the structure of a reproducing kernel Hilbert space of functions on $\Omega$. We further give an explicit formula for the kernel, and for the corresponding isometric isomorphism. Applications are given to Hilbert spaces associated to families of Gaussian processes.
Details
- Title: Subtitle
- Reproducing Kernel Hilbert Space vs. Frame Estimates
- Creators
- Palle E. T Jorgensen - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Mathematics, Vol.3(3), pp.615-625
- DOI
- 10.3390/math3030615
- ISSN
- 2227-7390
- eISSN
- 2227-7390
- Publisher
- Multidisciplinary Digital Publishing Institute
- Language
- English
- Date published
- 07/01/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9984241149602771
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