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Reproducing Kernel Hilbert Space vs. Frame Estimates
Journal article   Open access

Reproducing Kernel Hilbert Space vs. Frame Estimates

Mathematics, Vol.3(3), pp.615-625
07/01/2015
DOI: 10.3390/math3030615
url
https://doi.org/10.3390/math3030615View
Published (Version of record) Open Access

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.
frames Functional Analysis Hilbert space Karhunen Loève Mathematics reproducing kernel

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