May 2024 Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures
Johanna Ziegel, David Ginsbourger, Lutz Dümbgen
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Bernoulli 30(2): 1441-1457 (May 2024). DOI: 10.3150/23-BEJ1639

Abstract

We present new classes of positive definite kernels on non-standard spaces that are integrally strictly positive definite or characteristic. In particular, we discuss radial kernels on separable Hilbert spaces, and introduce broad classes of kernels on Banach spaces and on metric spaces of strong negative type. The general results are used to give explicit classes of kernels on separable Lp spaces and on sets of measures.

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Johanna Ziegel. David Ginsbourger. Lutz Dümbgen. "Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures." Bernoulli 30 (2) 1441 - 1457, May 2024. https://doi.org/10.3150/23-BEJ1639

Information

Received: 1 June 2022; Published: May 2024
First available in Project Euclid: 31 January 2024

MathSciNet: MR4699559
Digital Object Identifier: 10.3150/23-BEJ1639

Keywords: Characteristic kernel , integrally strictly positive definite kernel , kernel on Banach space , kernel on Hilbert space , kernel on measures

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Vol.30 • No. 2 • May 2024
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