New Directions in Frame Theory and Harmonic Analysis — The Legacy of Jean-Pierre Gabardo

Over the course of his distinguished career, Jean-Pierre Gabardo (1958-2024) had a substantial impact on the field of harmonic analysis and on analysis more generally, with his deep, original results in classical harmonic analysis, functional analysis, and spectral-tile duality; in diverse areas of geometric analysis; and in the newly developed area of non-commutative harmonic analysis. This volume is a tribute to his work and legacy, featuring chapters that reflect his mathematical interests, written by his colleagues and friends.An introductory chapter summarizes his broad and varied mathematical work and highlights his remarkable contributions as a mathematical mentor. The articles in the book are grouped into three focus points—functional and harmonic analysis, analysis of frames and non-orthogonal expansions, and diverse areas of sampling and spectral theory—and explore Gabardo’s contributions to these areas, as well as some related and current developments.