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Harmonic Analysis and Applications

In Honor of John J. Benedetto

  • Book
  • © 2006

Overview

Editors:
  1. Christopher Heil

    1. School of Mathematics, Georgia Institute of Technology, Atlanta, USA

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  • The text examines a wide range of topics in harmonic analysis and related areas, including frame theory, weighted-norm inequalities, wavelet theory, time-frequency analysis, and sampling theory.
  • Contributors are prominent, well-respected researchers and professionals in the field of harmonic analysis.
  • The book provides authoritative expositions that will be of lasting interest.
  • Excellent reference for graduate students, researchers, and professionals in mathematics, engineering, and physics.

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

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xxix
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  2. Harmonic Analysis

    1. Front Matter

      Pages 1-1
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    2. The Gibbs Phenomenon in Higher Dimensions

      • George Benke
      Pages 3-16

    3. Weighted Sobolev Inequalities for Gradients

      • Hans P. Heinig
      Pages 17-23

    4. Semidiscrete Multipliers

      • Georg Zimmermann
      Pages 25-48

  3. Frame Theory

    1. Front Matter

      Pages 49-49
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    2. A Physical Interpretation of Tight Frames

      • Peter G. Casazza, Matthew Fickus, Jelena Kovačević, Manuel T. Leon, Janet C. Tremain
      Pages 51-76

  4. Time-Frequency Analysis

    1. Front Matter

      Pages 77-77
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    2. Recent Developments in the Balian-Low Theorem

      • Wojciech Czaja, Alexander M. Powell
      Pages 79-100

    3. Some Problems Related to the Distributional Zak Transform

      • Jean-Pierre Gabardo
      Pages 101-126

    4. Gabor Duality Characterizations

      • Eric Hayashi, Shidong Li, Tracy Sorrells
      Pages 127-137

    5. A Pedestrian’s Approach to Pseudodifferential Operators

      • Karlheinz Gröchenig
      Pages 139-169

    6. Linear Independence of Finite Gabor Systems

      • Christopher Heil
      Pages 171-206

  5. Wavelet Theory

    1. Front Matter

      Pages 207-207
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    2. Explicit Cross-Sections of Singly Generated Group Actions

      • David Larson, Eckart Schulz, Darrin Speegle, Keith F. Taylor
      Pages 209-230

    3. The Theory of Wavelets with Composite Dilations

      • Kanghui Guo, Demetrio Labate, Wang-Q Lim, Guido Weiss, Edward Wilson
      Pages 231-250

  6. Sampling Theory and Shift-Invariant Spaces

    1. Front Matter

      Pages 251-251
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    2. Periodic Nonuniform Sampling in Shift-Invariant Spaces

      • Jeffrey A. Hogan, Joseph D. Lakey
      Pages 253-287

    3. Sampling on Unions of Shifted Lattices in One Dimension

      • Bjarte Rom, David Walnut
      Pages 289-323

    4. Learning the Right Model from the Data

      • Akram Aldroubi, Carlos Cabrelli, Ursula Molter
      Pages 325-333
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Keywords

About this book

This volume is dedicated to John Benedetto. It seems just yesterday that we celebrated his 60th birthday in a memorable conference in College Park. Yet that was October of 1999, and already more than six years have passed. But John is still too young to be fully honored by a single foreword,or even a singlevolume,thatattemptstosummarizetheimpactofhisworkonharmonic analysis, his students, and his coworkers.Given his continuing high (and even increasing) level of activities, his list of “lifetime achievements” is surely far from complete. Even so, we will make an attempt in this foreword to take a look back, to see the major lines of his work and activities during the past 40 years of his life as a scientist, and to learn from his biography (and bibliography) how the ?eld of harmonic analysis has changed over the years, and in particular to see the vibrant role that John has taken in this process. John’s ?rst paper appeared in 1965, when he was 25 years old, and his ?rst book (the Springer Lecture Notes on Harmonic Analysis on Totally D- connected Sets) when he was 31. By that time he had already published on the subjects of Tauberian algebras, in the theory of generalized functions, and on questions related to spectral synthesis. His work on this latter topic continued through the 1970s, culminating in the insightful volume Spectral Synthesis (1975). Only a year later, his text Real Variables and Integration with Historical Notes appeared.

Editors and Affiliations

  • School of Mathematics, Georgia Institute of Technology, Atlanta, USA

    Christopher Heil

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