English

Schoenberg Representations and Gramian Matrices of Mat\'ern Functions

Classical Analysis and ODEs 2017-02-21 v1

Abstract

We represent Mat\'ern functions in terms of Schoenberg's integrals which ensure the positive definiteness and prove the systems of translates of Mat\'ern functions form Riesz sequences in L2(Rn)L^2(\R^n) or Sobolev spaces. Our approach is based on a new class of integral transforms that generalize Fourier transforms for radial functions. We also consider inverse multi-quadrics and obtain similar results.

Keywords

Cite

@article{arxiv.1702.05894,
  title  = {Schoenberg Representations and Gramian Matrices of Mat\'ern Functions},
  author = {Yong-Kum Cho and Dohie Kim and Kyungwon Park and Hera Yun},
  journal= {arXiv preprint arXiv:1702.05894},
  year   = {2017}
}