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 |
Preview |
PDF
- Published Version
Available under License Creative Commons Attribution. Download (1MB) | Preview |
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 |
Actions (repository staff only)
Edit Item |