Isometric representation of integral operators with positive-semidefinite kernels - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... (Preprint) Year : 2023

Isometric representation of integral operators with positive-semidefinite kernels

Abstract

We describe a natural coisometry from the Hilbert space of all Hilbert- Schmidt operators on a separable reproducing kernel Hilbert space (RKHS) H, and onto the RKHS G associated with the squared-modulus of the reproducing kernel of H. We discuss the properties of this coisometry, and show that trace-class integral operators defined by general measures and the reproducing kernel of H always belong to its initial space. The images of such operators are the Riesz representations of integral functionals on G, drawing a direct connection between the approximation of trace-class integral operators with PSD kernels and the approximation of integral functionals on RKHSs associated with squared-modulus kernels.
Fichier principal
Vignette du fichier
Iso_Rep_RKHS.pdf (362.39 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03848105 , version 1 (10-11-2022)
hal-03848105 , version 2 (30-04-2023)

Identifiers

  • HAL Id : hal-03848105 , version 2

Cite

Bertrand Gauthier. Isometric representation of integral operators with positive-semidefinite kernels. 2023. ⟨hal-03848105v2⟩

Collections

INSMI
81 View
80 Download

Share

Gmail Facebook X LinkedIn More