During his long and distinguished career, J. Rowland Higgins (1935-2020) made a substantial impact on many mathematical fields through his work on sampling theory, his deep knowledge of its history, and his service to the community. This volume is a tribute to his work and legacy, featuring chapters written by distinguished mathematicians that explore cutting-edge research in sampling, approximation, signal analysis, and other related areas. An introductory chapter provides a biography of Higgins that explores his rich and unique life, along with a bibliography of his papers; a brief history of the SampTA meetings - of which he was a Founding Member - is also included. The remaining articles are grouped into four sections - classical sampling, theoretical extensions, frame theory, and applications of sampling theory - and explore Higgins' contributions to these areas, as well as some of the latest developments.
Inhaltsverzeichnis
PART I: Classical Sampling - Classical and approximate exponential sampling formula: their interconnections in uniform and Mellin Lebesgue norms (Schmeisser). - Asymptotic theorems for Durrmeyer sampling operators with respect to the L-norm (Vinti). - On generalized Shannon sampling operators in the cosine operator function framework (Kivinukk). - Bernstein spaces, sampling, and Riesz-Boas interpolation formulas in Mellin Analysis (Pesenson). - The behavior of frequency band limited cardinal interpolants(Madych). - The Balian-Low theorem for (Cq)-systems in shift-invariant spaces (owell). - Whittaker - type derivative sampling and (p; q) - order weighted diffrential operator (Pogány). - Shannon Sampling via Poisson, Cauchy, Jacobi and Levin (Casey). - Part (II.) Theoretical Extensions - Schoenberg s Theory of Totally Positive Functions and the Riemann Zeta Function (Gröchenig). - Sampling via the Banach Gelfand Triple (Feichtinger). - Part (III.) Frame Theory - A Survey of FusionFrames in Hilbert Spaces (Köhldorfer). - Frames of iterations and vector-valued model spaces (Cabrelli). - A survey on frame representations and operator orbits (Christensen). - Three proofs of the Benedetto Fickus theorem (Mixon). - Clifford Prolate SpheroidalWavefunctions and Associated Shift Frames (Lakey). - Part (IV.) Applications - Power Aware Analog To Digital Converters (Mulleti). - Quaternionic coupled fractional Fourier transform on Boehmians (Zayed). - Sampling : Theory and Applications A History of the SampTA Meetings (Casey). - Accelerartion Algorithms for Iterative Methods (Marvasti).
