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Mathematics 2015, 3(3), 615-625; doi:10.3390/math3030615

Reproducing Kernel Hilbert Space vs. Frame Estimates

1
Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA
2
Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Box 1653, Edwardsville, IL 62026, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Lokenath Debnath
Received: 21 May 2015 / Revised: 3 July 2015 / Accepted: 3 July 2015 / Published: 8 July 2015
View Full-Text   |   Download PDF [222 KB, uploaded 8 July 2015]

Abstract

We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn H into a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω . We then identify conditions on these functions which automatically give H the structure of a reproducing kernel Hilbert space of functions on Ω. 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. View Full-Text
Keywords: Hilbert space; frames; reproducing kernel; Karhunen-Loève Hilbert space; frames; reproducing kernel; Karhunen-Loève
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Jorgensen, P.E.T.; Song, M.-S. Reproducing Kernel Hilbert Space vs. Frame Estimates. Mathematics 2015, 3, 615-625.

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