Document Type
Article
Publication Date
Summer 7-8-2015
Department
Mathematics & Statistics
Abstract
We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn Hinto 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.
Recommended Citation
Jorgensen, Palle E. T. and Song, Myung-Sin, "Reproducing Kernel Hilbert Space vs. Frame Estimates" (2015). SIUE Faculty Research, Scholarship, and Creative Activity. 8.
https://spark.siue.edu/siue_fac/8
Comments
© 2015 by the authors; Originally published in Mathematics (ISSN 2227-7390), licensee MDPI, Basel, Switzerland, available online at http://dx.doi.org/10.3390/math3030615.
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/).