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Full Description
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.
Contents
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).
