Stephen D. Casey & M. Maurice Dodson 
Sampling, Approximation, and Signal Analysis 
Harmonic Analysis in the Spirit of J. Rowland Higgins

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 Samp TA 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.

Spis treści

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 Fusion Frames 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 Spheroidal Wavefunctions 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 Samp TA Meetings (Casey).- Accelerartion Algorithms for Iterative Methods (Marvasti).

O autorze

Stephen D. Casey is a Professor of Mathematics at American University. His work includes multichannel deconvolution and multi-rate sampling, sampling in Euclidean and non-Euclidean geometries, sampling for wideband signals, signal adaptive frame theory, and the analysis of pulse train signals. He has published over 70 articles and edited two books, and has given over one hundred and twenty talks. His research has been funded by twenty-four research grants and four contracts, and he was awarded three provisional patents and two full patents for work in signal processing. He received the 2019 Drew University Alumni Achievement Award in the Sciences.





​Maurice Dodson is a Professor Emeritus of Mathematics at the University of York. He wrote over seventy papers, co-authored 1 book and co-edited another. His interests broadened to Diophantine approximation and the metrical theory and further to dynamical systems and their many applications, including the WKS sampling theorem and its variety of applications, the last stemming from a connection with X-ray  crystallography. This led to meeting Rowland Higgins in 1985 and the start of a long productive collaboration, often with a number of authors, in sampling theory and its applications and extensions, particularly to LCA groups and Kluvanek’s theorem and to sampling for function spaces. 



Paulo Jorge S. G. Ferreira is a Professor of Electrical Engineering at University of Aveiro, Portugal. He serves as Rector of the University of Aveiro since May 2022, in his second term. He has been editor of international scientific journals in engineering and mathematics and he is author or co-author of works published in well-known scientific journals in the fields of Electrical Engineering, Computer Science, Agriculture, Bioinformatics, Mathematics, Physics and other fields. He is listed in the top 1% cited scientists in the so-called Stanford Ranking (’Updated science-wide author databases of standardized citation indicators’, 2022).







Ahmed I. Zayed is a Professor of Mathematics at the Department of Mathematical Sciences, De Paul University, Chicago, and was the Chair of the department from 2001 until 2021. His research interest is applied harmonic analysis, sampling, and integral transforms. He has published 2 books and edited 7 research monographs. He has written 22 book chapters, published 118 research articles, and reviewed 173 publications for the Mathematical Reviews and 81 for the Zentralblatt für Mathematik (zb Math). He has served on the editorial boards of 22 scientific research journals.