Schur's orthogonality relations for the free group

TL;DR

This paper establishes explicit convergence results for integrals involving coefficients of the quasi-regular representation of free groups, enhancing understanding of harmonic analysis on these groups.

Contribution

It provides explicit convergence of normalized integrals of representation coefficients on free groups, a novel result in harmonic analysis.

Findings

Explicit convergence of integrals on free group balls

Enhanced understanding of representation coefficients

New orthogonality relations for free groups

Abstract

Explicit convergence of suitably normalized integrals on balls where the integrand is the product of coefficients of the quasi-regular representation of the finitely generated free group.