English

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}
}
R2 v1 2026-06-21T23:28:09.976Z