Sampling, Frames, and Harmonic Analysis
Description
This edited volume presents a collection of research articles written in honor of Akram Aldroubi that highlight his profound and enduring influence on multiple areas of modern analysis and its applications. Written by leading mathematicians, these articles address recent advances in sampling theory, frame theory, wavelet analysis, signal and image processing, data science, and other areas of applied and computational harmonic analysis.
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Content
Preface.- Independent Random Variables and Classical Analysis.- Linear Independence of Finite Gabor Systems: Updates, Comparisons, Directions.- The Concept of Wiener Amalgam Spaces.- Gabor Frames and Modulation Spaces.- Quantum Paving: When Sphere Packings Meet Gabor Frames.- H¨older-Continuity of Extreme Spectral Values of Pseudodifferential
Operators, Gabor Frame Bounds, and Saturation.- Bridging: Past, Present, and Future.- Four Problems in Frame Theory.- Convolutional Dynamical Sampling and Some New Results.- Parseval Convolution Operators and Neural Networks.- Sparse Recovery for Overcomplete Frames: Sensing Matrices and Recovery Guarantees.- Multifractal Analysis Based on Weak Scaling Exponents: Applications to MEG Recordings in Neuroscience.- Data representation with optimal transport.- Kernel-Based Sampling and Inference: An Applications Based Dichotomy.- On Sylvester Equations in Banach Subalgebras.- Method of similar operators in harmonious Banach spaces.- The Non-Definability of the Spaces of Tsirelson and Schlumprecht.