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arXiv · 1702.05894

Schoenberg Representations and Gramian Matrices of Mat\'ern Functions

Yong-Kum Cho·Dohie Kim·Kyungwon Park·Hera Yun
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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 $L^2(\R^n)$ 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.

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Yong-Kum Cho, Dohie Kim, Kyungwon Park, Hera Yun. 2017-02-20. Schoenberg Representations and Gramian Matrices of Mat\'ern Functions. https://arxiv.org/abs/1702.05894

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