H.G. Feichtinger: Foreword C. Heil: Preface The Benedetto Mathematical Family Tree Publications of John J. Benedetto ------------------ Part I. Harmonic Analysis G. Benke: The Gibbs Phenomenon in Higher Dimensions H.P. Heinig: Weighted Sobolev Inequalities for Gradients G. Zimmermann: Semidiscrete Multipliers ----------------- Part II. Frame Theory P.G. Casazza, M. Fickus, J. Kovacevic, M.T. Leon, and J.C. Tremain: A Physical Interpretation of Tight Frames ----------------- Part III. Time-Frequency Analysis W. Czaja and A.M. Powell: Recent Developments in the Balian-Low Theorem J.-P. Gabardo: Some Problems Related to the Distributional Zak Transform E. Hayashi, S. Li, and T. Sorrells: Gabor Duality Characterizations K. Gröchenig: A Pedestrian's Approach to Pseudodifferential Operators C. Heil: Linear Independence of Finite Gabor Systems ----------------- Part IV. Wavelet Theory D. Larson, E. Schulz, D. Speegle, and K.F. Taylor: Explicit Cross-Sections of Singly Generated Group Actions K. Guo, D. Labate, W.-Q Lim, G. Weiss, and E. Wilson: The Theory of Wavelets with Composite Dilations ------------------- Part V. Sampling Theory and Shift-Invariant Spaces J.A. Hogan and J.D. Lakey: Periodic Nonuniform Sampling in Shift-Invariant Spaces B. Rom and D. Walnut: Sampling on Unions of Shifted Lattices in One Dimension A. Aldroubi, C. Cabrelli, and U. Molter: Learning the Right Model from the Data L. Baggett: Redundancy in the Frequency Domain P.G. Casazza, O. Christensen, S. Li, and A. Lindner:Density Results for Frames of Exponentials ------------------ Index

This self-contained volume in honor of John J. Benedetto covers a wide range of topics in harmonic analysis and related areas. These include weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected are written by prominent researchers and professionals in the field. The book pays tribute to John J. Benedetto's achievements and expresses an appreciation for the mathematical and personal inspiration he has given to so many students, co-authors, and colleagues.