Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures

Ziegel, Johanna; Ginsbourger, David; Dümbgen, Lutz (2024). Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures. Bernoulli, 30(2), pp. 1441-1457. International Statistical Institute 10.3150/23-BEJ1639

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Ziegel, Johanna F., Ginsbourger, David, Dümbgen, Lutz

Subjects:

500 Science > 510 Mathematics

ISSN:

1350-7265

Publisher:

International Statistical Institute

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

05 Feb 2024 16:28

Last Modified:

06 Feb 2024 04:28

Publisher DOI:

10.3150/23-BEJ1639

BORIS DOI:

10.48350/192423

URI:

https://boris.unibe.ch/id/eprint/192423

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