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

Bertrand Gauthier (1)

1 School of Mathematics [Cardiff]

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. Through this coisometry, trace-class integral operators defined by general measures and the reproducing kernel of H are isometrically represented as potentials in G, and the quadrature approximation of these operators is equivalent to the approximation of integral functionals on G. 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.

Mots clés: reproducing kernel Hilbert spaces; integral operators; low-rank approximation; kernel embedding of measures; differentiable relaxation

Domaines: Mathématiques [math]

Bertrand Gauthier. Kernel embedding of measures and low-rank approximation of integral operators. Positivity, 2024, 28 (2), pp.29. ⟨10.1007/s11117-024-01041-8⟩. ⟨hal-03848105v3⟩