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arXiv · 2102.10628

Bumps and polynomials in RKHSs of translation-invariant kernels

Toni Karvonen
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Abstract

We use the uncertainty principle of harmonic analysis and the Beurling-Malliavin theorem to describe when a reproducing kernel Hilbert space of a translation-invariant positive-definite kernel contains bump functions and polynomials. How fast the spectral density of the kernel decays controls whether or not these functions are included in the Hilbert space.

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Toni Karvonen. 2021-02-21. Bumps and polynomials in RKHSs of translation-invariant kernels. https://arxiv.org/abs/2102.10628

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