Twentieth Century Harmonic Analysis: A Celebration

ISBN-13: 9780792371687 / Angielski / Twarda / 2001 / 412 str.

James S. Byrnes; J. S. Byrnes; J. S. Byrnes

Opis

Almost a century ago, harmonic analysis entered a (still continuing) Golden Age, with the emergence of many great masters throughout Europe. They created a wealth of profound analytic methods, to be successfully exploited and further developed by succeeding generations. This flourishing of harmonic analysis is today as lively as ever, as the papers presented here demonstrate. In addition to its own ongoing internal development and its basic role in other areas of mathematics, physics and chemistry, financial analysis, medicine, and biological signal processing, harmonic analysis has made fundamental contributions to essentially all twentieth century technology-based human endeavours, including telephone, radio, television, radar, sonar, satellite communications, medical imaging, the Internet, and multimedia. This ubiquitous nature of the subject is amply illustrated. The book not only promotes the infusion of new mathematical tools into applied harmonic analysis, but also to fuel the development of applied mathematics by providing opportunities for young engineers, mathematicians and other scientists to learn more about problem areas in today's technology that might benefit from new mathematical insights.

Spis treści

Dedication. Preface. Part 1: The Papers. On the Uncertainty Principle in Harmonic Analysis; V.P. Havin. Operator Theory and Harmonic Analysis; H.S. Shapiro. Probabilities and Baire's theory in harmonic analysis; J.-P. Kahane. Representations of Gabor frame operators; A.J.E.M. Janssen. Does Order Matter; T.W. Körner. Wavelet expansions, function spaces and multifractial analysis; S. Jaffard. Some Plots of Bessel Functions of Two Variables; F.A. Grünbaum. Lesser Known FFT Algorithms; R. Tolimieri, M. An. The Phase Problem of X-ray Crystallography; H.A. Hauptman. Multiwindow Gabor-type Representations and Signal Representation by Partial Information; Y.Y. Zeevi. Some polynomial extremal problems which emerged in the twentieth century; B. Saffari. The Problem of Efficient Inversions and Bezout Equations; N. Nikolski. Harmonic Analysis as found in Analytic Number Theory; H.L. Montgomery. Mathematics of Radar; B. Moran. The Mathematical Theory of Wavelets; G. Weiss, E.N. Wilson. Part 2: Problems. Assorted Problems; Various authors. How to Use the Fourier Transform in Asymptotic Analysis; V. Gurarii, et al. Index.