Reproducing Kernel Hilbert Space vs. Frame Estimates

2016/06/15 by Jorgensen, Palle E. T., Song, Myung-Sin
#42C40 #46L60 #46L89 #47S50 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1606.04868

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.

Related

• Frames, their relatives and reproducing kernel Hilbert spaces
• Frame analysis and approximation in reproducing kernel Hilbert spaces
• When does a Gaussian process have its paths in a reproducing kernel Hilbert space?
• Four Properties of Reproducing Kernel Hilbert Spaces
• A Primer on Reproducing Kernel Hilbert Spaces