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Birkhäuser

Sampling, Approximation, and Signal Analysis

Harmonic Analysis in the Spirit of J. Rowland Higgins

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  • © 2023

Overview

Editors:
  1. Stephen D. Casey

    1. Department of Mathematics and Statistics, American University, Washington, DC, USA

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  2. M. Maurice Dodson

    1. Department of Mathematics, University of York, York, UK

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  3. Paulo J. S. G. Ferreira

    1. IEETA, University of Aveiro, Aveiro, Portugal

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  4. Ahmed Zayed

    1. Department of Mathematical Sciences, DePaul University, Chicago, USA

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  • Highlights the many significant mathematical contributions of J. Rowland Higgins
  • Explores the latest developments in sampling theory and its applications
  • Features chapters written by distinguished mathematicians

Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xxxiv
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  2. Classical Sampling

    1. Front Matter

      Pages 1-1
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    2. Classical and Approximate Exponential Sampling Formula: Their Interconnections in Uniform and Mellin–Lebesgue Norms

      • C. Bardaro, P. L. Butzer, I. Mantellini, G. Schmeisser, R. L. Stens
      Pages 3-22

    3. Asymptotic Theorems for Durrmeyer Sampling Operators with Respect to the \(L^p\)-Norm

      • Danilo Costarelli, Gianluca Vinti
      Pages 23-38

    4. On Generalized Shannon Sampling Operators in the Cosine Operator Function Framework

      • Andi Kivinukk, Gert Tamberg
      Pages 39-68

    5. Bernstein Spaces, Sampling, and Riesz-Boas Interpolation Formulas in Mellin Analysis

      • Isaac Z. Pesenson
      Pages 69-88

    6. The Behavior of Frequency Bandlimited Cardinal Interpolants

      • W. R. Madych
      Pages 89-111

    7. The Balian-Low Theorem for \((C_q)\)-Systems in Shift-Invariant Spaces

      • Alexander M. Powell
      Pages 113-129

    8. Whittaker-Type Derivative Sampling and \((p, q)\)-Order Weighted Differential Operator

      • Tibor K. Pogány
      Pages 131-138

    9. Shannon Sampling Theorem via Poisson, Cauchy, Jacobi, and Levin

      • Stephen D. Casey
      Pages 139-189

  3. Theoretical Extensions

    1. Front Matter

      Pages 191-191
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    2. Schoenberg’s Theory of Totally Positive Functions and the Riemann Zeta Function

      • Karlheinz Gröchenig
      Pages 193-210

    3. Sampling via the Banach Gelfand Triple

      • Hans G. Feichtinger
      Pages 211-242

  4. Frame Theory

    1. Front Matter

      Pages 243-243
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    2. A Survey of Fusion Frames in Hilbert Spaces

      • L. Köhldorfer, P. Balazs, P. Casazza, S. Heineken, C. Hollomey, P. Morillas et al.
      Pages 245-328

    3. Frames of Iterations and Vector-Valued Model Spaces

      • Carlos Cabrelli, Ursula Molter, Daniel Suárez
      Pages 329-348

    4. A Survey on Frame Representations and Operator Orbits

      • Ole Christensen, Marzieh Hasannasab
      Pages 349-370

    5. Three Proofs of the Benedetto–Fickus Theorem

      • Dustin G. Mixon, Tom Needham, Clayton Shonkwiler, Soledad Villar
      Pages 371-391

    6. Clifford Prolate Spheroidal Wavefunctions and Associated Shift Frames

      • Hamed Baghal Ghaffari, Jeffrey A. Hogan, Joseph D. Lakey
      Pages 393-411

  5. Applications

    1. Front Matter

      Pages 413-413
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics and Statistics, American University, Washington, DC, USA

    Stephen D. Casey

  • Department of Mathematics, University of York, York, UK

    M. Maurice Dodson

  • IEETA, University of Aveiro, Aveiro, Portugal

    Paulo J. S. G. Ferreira

  • Department of Mathematical Sciences, DePaul University, Chicago, USA

    Ahmed Zayed

About the editors

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, DePaul 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 (zbMath). He has served on the editorial boards of 22 scientific research journals. 

  


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