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

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.