Journal article
Sampling with positive definite kernels and an associated dichotomy
Advances in theoretical and mathematical physics, Vol.24(1), pp.125-154
01/01/2020
DOI: 10.4310/ATMP.2020.v24.n1.a4
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 H(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.
Details
- Title: Subtitle
- Sampling with positive definite kernels and an associated dichotomy
- Creators
- Palle Jorgensen - Univ Iowa, Dept Math, Iowa City, IA 52242 USAJames Tian - Mathematical Reviews, Ann Arbor, Michigan, U.S.A.
- Resource Type
- Journal article
- Publication Details
- Advances in theoretical and mathematical physics, Vol.24(1), pp.125-154
- Publisher
- INT PRESS BOSTON, INC
- DOI
- 10.4310/ATMP.2020.v24.n1.a4
- ISSN
- 1095-0761
- eISSN
- 1095-0753
- Number of pages
- 30
- Language
- English
- Date published
- 01/01/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984240862802771
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