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Description
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.
Translational tiles of R × Z2 and wavelet sets in the form of two intervals.- Quantum Gabor frame on LCA groups.- Beurling densities and frames of exponentials on the union of small balls.- The Zak transform and rationally sampled Gabor analysis.- Scalable Frames in Shift invariant spaces.- Trichotomy for the HRT Conjecture for mixed integer configuration.- Generalization of the Three Squares Theorem.- Nuclear Spaces and a Banach-Saks Theorem.- Brownian Motions on Sierpinski Carpets: A survey.- Normal dilations for bounded linear maps on von Neumann algebras.- Absolute continuity and the classical uncertainty principle.- Towards direct L2-bounds for maximal partial sums of Walsh Fourier series: The case of dyadic partial sums.- Additive energy, uncertainty principle and signal recovery mechanism.- Beyond Carleman linearization of non linear dynamical system: Insight from a case study.- Phase Retrieval for STLCT: Inverse Formula and Uniqueness Sets.- The tail null space property and stability for the tail-minimization approach in compressed sensing.- Erasure reconstruction from sample data using alternating summation kernels.Erasure reconstruction from sample data using alternating summation kernels.- Entropy, moments, effective resistance, and harmonic morphisms on edge-weighted graphs.- A numerical solution based on the fractional shifted Vieta-Lucas polynomials for solving fractional Volterra integral equations.
