Harmonic Analysis -- The Gibbs Phenomenon in Higher Dimensions -- Weighted Sobolev Inequalities for Gradients -- Semidiscrete Multipliers -- Frame Theory -- A Physical Interpretation of Tight Frames -- 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 -- Wavelet Theory -- Explicit Cross-Sections of Singly Generated Group Actions -- The Theory of Wavelets with Composite Dilations -- 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.

John J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. This self-contained volume in honor of John covers a wide range of topics in harmonic analysis and related areas, including weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The invited chapters pay tribute to John’s many achievements and express an appreciation for both the mathematical and personal inspiration he has given to so many students, coauthors, and colleagues. 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 book is divided into the following five sections: * Classical harmonic analysis * Frame theory * Time-frequency analysis * Wavelet theory * Sampling theory and shift-invariant spaces Harmonic Analysis and Applications is an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics. Contributors: A. Aldroubi, L. Baggett, G. Benke, C. Cabrelli, P.G. Casazza, O. Christensen, W. Czaja, M. Fickus, J.-P. Gabardo, K. Gröchenig, K. Guo, E. Hayashi, C. Heil, H.P. Heinig, J.A. Hogan, E. Kovacevic, D. Labate, J.D. Lakey, D. Larson, M.T. Leon, S. Li, W.-Q Lim, A. Lindner, U. Molter, A.M. Powell, B. Rom, E. Schulz, T. Sorrells, D. Speegle, K.F. Taylor, J.C. Tremain, D. Walnut, G. Weiss, E. Wilson, G. Zimmermann