Sampling with positive definite kernels and an associated dichotomy

2017/08/20 by Jorgensen, Palle, Tian, Feng
#05C50 #05C75 #22E70 #31A15 #31C20 #42C15 #46N30 #46N50 #58J65 #65R10 #81S25 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47L60 #Secondary 46N20

paper · doi:10.48550/arxiv.1708.06016

Abstract

We study classes of reproducing kernels K on general domains; these are kernels which arise commonly in machine learning models; models based on certain families of reproducing kernel Hilbert spaces. They are the positive definite kernels K with the property that there are countable discrete sample-subsets S; i.e., proper subsets S having the property that every function in \mathscrH(K) admits an S-sample representation. We give a characterizations of kernels which admit such non-trivial countable discrete sample-sets. A number of applications and concrete kernels are given in the second half of the paper.

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