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This volume, in honor of John J. Benedetto on the occasion of his 65th birthday, features invited articles covering a wide range of topics in areas where he has made fundamental and lasting contributions, such as harmonic analysis, number theory, weighted norm inequalities, wavelet theory, time-frequency analysis, and sampling theory.
Although the scope of the book is broad, chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected here are written by prominent, well-respected researchers and professionals in the field.
List of contents
Foreword.- Preface.- The Benedetto Mathematical Family Tree.- Publications of John J. Benedetto.- Part I. Harmonic Analysis.- The Gibbs Phenomenon in Higher Dimensions.- Weighted Sobolev Inequalities for Gradients.- Semidiscrete Multipliers.- Part II. Frame Theory.- A Physical Interpretation of Tight Frames.- Part III. Time-Frequency Analysis.- Recent Developments in the Balian Low Theorem.- Some Problems Related to the Distributional Zak Transform.- Gabor Duality Characterizations.- A Pedestrian's Approach to Pseudodifferential Operators.- Linear Independence of Finite Gabor Systems.- Part IV. Wavelet Theory.- Explicit Cross-Sections of Singly Generated Group Actions.- The Theory of Wavelets with Composite Dilations.- Part V. Sampling Theory and Shift-Invariant Spaces.- Periodic Nonuniform Sampling in Shift-Invariant Spaces.- Sampling on Unions of Shifted Lattices in One Dimension.- Learning the Right Model from the Data.- Redundancy in the Frequency Domain.- Density Results for Frames of Exponentials.- Index
Summary
This self-contained volume in honor of John J. Benedetto examines a wide range of topics in harmonic analysis and related areas. These include frame theory, weighted-norm inequalities, wavelet theory, time-frequency analysis, and sampling theory. Although the scope of the book is broad, chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected here are written by prominent, well-respected researchers and professionals in the field of harmonic analysis. The invited chapters pay tribute to John J. Benedetto’s many achievements and express an appreciation for both the mathematical and personal inspiration he has given to so many students, coauthors, and colleagues. The book is an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.
