Sub-exponentially localized kernels and frames induced by orthogonal expansions

TL;DR

This paper develops sub-exponentially localized kernels and frames for classical orthogonal expansions, enhancing the mathematical tools available for analysis in these function spaces.

Contribution

It introduces a novel construction of localized kernels and frames specifically tailored for Jacobi polynomials, spherical harmonics, and other classical orthogonal systems.

Findings

Constructed sub-exponentially localized kernels for various orthogonal systems

Established frames with improved localization properties

Extended the theory to Hermite and Laguerre functions

Abstract

The aim of this paper is to construct sup-exponentially localized kernels and frames in the context of classical orthogonal expansions, namely, expansions in Jacobi polynomials, spherical harmonics, orthogonal polynomials on the ball and simplex, and Hermite and Laguerre functions.