Abstract

Kernel-based methods provide a powerful and flexible framework for addressing histopolation problems, where the input data consists of average values of a function over intervals or higher-dimensional regions rather than pointwise samples. This presentation introduces the concept of Averaging Kernel Hilbert Spaces (AKHS), a natural extension of classical Reproducing Kernel Hilbert Spaces (RKHS) tailored to histopolation. Within this framework, we develop construction principles for averaging kernels. We establish a fundamental isometric isomorphism between an AKHS and an associated RKHS, which allows reformulating histopolation as an interpolation problem in the corresponding RKHS. This connection yields explicit expressions for the histopolation matrix, criteria for unisolvence, and convergence results for the mean values of the histopolants.

The presentation will briefly cover fundamental topics such as polynomial interpolation, Radial Basis Function (RBF) interpolation and the related challenges of optimizing node placement and the shape of basis functions.

The video of the seminar will appear shortly afterwards in this Mediaspace channel.

Seminario Dottorato