Kernel embedding of measures and low-rank approximation of integral operators

Gauthier, Bertrand ORCID: https://orcid.org/0000-0001-5469-814X 2024. Kernel embedding of measures and low-rank approximation of integral operators. Positivity 28 , 29. 10.1007/s11117-024-01041-8

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Abstract

We describe a natural coisometry from the Hilbert space of all Hilbert-Schmidt operators on a separable reproducing kernel Hilbert space and onto the RKHS associated with the squared-modulus of the reproducing kernel of . Through this coisometry, trace-class integral operators defined by general measures and the reproducing kernel of are isometrically represented as potentials in , and the quadrature approximation of these operators is equivalent to the approximation of integral functionals on . We then discuss the extent to which the approximation of potentials in RKHSs with squared-modulus kernels can be regarded as a differentiable surrogate for the characterisation of low-rank approximation of integral operators.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Publisher:	Springer Verlag
ISSN:	1385-1292
Date of First Compliant Deposit:	5 March 2024
Date of Acceptance:	23 February 2024
Last Modified:	08 Apr 2024 08:50
URI:	https://orca.cardiff.ac.uk/id/eprint/166863

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