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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

Operator theory --- Functional analysis --- Harmonic analysis. Fourier analysis --- Computer science --- Fourieranalyse --- analyse (wiskunde) --- functies (wiskunde) --- informatica

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Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey's scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.

Harmonic analysis. Fourier analysis --- Numerical analysis --- Mathematics --- Computer science --- Fourieranalyse --- functies (wiskunde) --- informatica --- wiskunde --- numerieke analyse

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Operator theory --- Functional analysis --- Harmonic analysis. Fourier analysis --- Computer science --- Fourieranalyse --- analyse (wiskunde) --- functies (wiskunde) --- informatica

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Ordered algebraic structures --- Harmonic analysis. Fourier analysis --- Mathematics --- Fourieranalyse --- algebra --- wiskunde

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With the exception of the tragedy on September 11, the year 2001 was relatively normal and uneventful: remember, this should have been the year of the Clarke's andKubrick's Space Odyssey, mission to Juiter; it should have been the year of the HAL-9000 computer. Today, the Personal Computer is as ubiquitous and omnipresent as was HAL on the Discovery spaceship. And the rate of technology development and market growth in electronics industry still follows the famous ˜Moore Law', almost four decades after it has been first formulated: in 1965, Gordon Moore of Intel Corporation predicted the doubling of the number of transistors on a chip every 2 years, corrected to 18 months in 1967; at that time, the landing on the Moon was in full preparation. Curiously enough, today noone cares to go to the Moon again, let alone Jupiter. And, in spite of all the effort in digital engineering, we still do not have anything close to 0.1% of the HAL capacity (fortunately?!). Whilst there are many research labs striving to put artificial intelligence into a computer, there are also rumors that this has already happened (with Windows-95, of course!).

Functional analysis --- Harmonic analysis. Fourier analysis --- Electronics --- Electrical engineering --- Computer. Automation --- Fourieranalyse --- functies (wiskunde) --- informatica --- elektronica --- elektrische circuits --- versterkers