On Translation Invariant Kernels and Screw Functions
Functional Analysis
2013-02-19 v1 Machine Learning
Machine Learning
Abstract
We explore the connection between Hilbertian metrics and positive definite kernels on the real line. In particular, we look at a well-known characterization of translation invariant Hilbertian metrics on the real line by von Neumann and Schoenberg (1941). Using this result we are able to give an alternate proof of Bochner's theorem for translation invariant positive definite kernels on the real line (Rudin, 1962).
Keywords
Cite
@article{arxiv.1302.4343,
title = {On Translation Invariant Kernels and Screw Functions},
author = {Purushottam Kar and Harish Karnick},
journal= {arXiv preprint arXiv:1302.4343},
year = {2013}
}