edited by James S. Byrnes
Prometheus Inc., Newport, RI; and University of Massachusetts, Boston, USA

Twentieth Century Harmonic Analysis ? A Celebration
Proceedings of the NATO Advanced Study Institute, held in Il Ciocco, Italy, 2-15 July 2000

NATO SCIENCE SERIES: II: Mathematics, Physics and Chemistry Volume 33

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.

Contents and Contributors
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. Korner. Wavelet expansions, function spaces and multifractial analysis; S. Jaffard. Some Plots of Bessel Functions of Two Variables; F.A. Grunbaum. 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.

Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-7168-2
Paperback, ISBN 0-7923-7169-0
September 2001, 424 pp.

P.M. Gadea / Instituto de Matematicas y Fisica Fundamental, Madrid, Spain
J. Munoz Masque /  Dept. de Tratamiento de la Informacion y Codificacion, Madrid, Spain

Analysis and Algebra on Differentiable Manifolds:
A Workbook for Students and Teachers

KLUWER TEXTS IN THE MATHEMATICAL SCIENCES Volume 23

This book is a collection of 375 completely solved exercises on differentiable manifolds, Lie groups, fibre bundles, and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools. It is the first book consisting of completely solved problems on differentiable manifolds, and therefore will be a complement to the books on theory. A 42-page formulary is included which will be useful as an aide-memoire, especially for teachers and researchers on these topics.

Audience: The book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics, and some branches of engineering.

Contents
Prologue. Preface. Acknowledgments. About the Authors. 1. Differentiable Manifolds. 2. Tensor Fields and Differential Forms. 3. Integration on Manifolds. 4. Lie Groups. 5. Fibre Bundles. 6. Riemannian Geometry. 7. Some Definitions and Theorems. 8. Some Formulas and Tables. 9**. Manual of `Superficies'. 10. Indices and Notations. References. List of Notations. List of Figures. Index. Ad 9** A CD-ROM is included with the application `Superficies' by Professor A. Montesinos.


Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 1-4020-0027-8
Paperback, ISBN 1-4020-0163-0
October 2001, 493 pp.