Schoenberg Representations and Gramian Matrices of Matérn Functions

Abstract

We represent Matérn functions in terms of Schoenberg's integrals which ensure the positive definiteness and prove the systems of translates of Matérn functions form Riesz sequences in $L^2({\mathbb{R}}^n)$ 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.

Cited by in corpus (1)

• Matrix valued positive definite kernels related to the generalized Aitken's integral for Gaussians