Kendrick Press, 2009. xiv + 688 pages. ISBN 0-9793183-9-4. $160.
This tribute to the great analyst Jean-Pierre Kahane comes a little late
for his eightieth birthday in December 2006. It will be welcomed by his
many admirers. The editor asked Professor Kahane to select his favorite
research papers to give a total of about 650 pages. The outcome consists
of the 63 papers, in English and French, in the present volume. Papers already
available in Salem's Collected Works were not included.
Mean periodic functions, pseudo-periodic functions, almost-periodic functions and quasi-analyticity are themes in the earlier papers. Another important topic is the converse to the
Wiener-Levy theorem. Of course there are papers on the convergence of Fourier series, along with problems of uniqueness and spectral synthesis. Symbolic calculus in Banach algebras, lacunary series, thin sets and trigonometric polynomials with unimodular coefficients are treated. There is a contribution on Hilbert's 13th problem.
Naturally, there are papers on random coverings, Brownian motion and multiplicative processes. We find a paper on a question of Bohr on Dirichlet series and one on an inverse Heisenberg inequality. The last paper in the volume concerns Beurling's theory of generalized prime numbers. There are riches here to appeal to any aficionado of mathematical analysis. Readers will enjoy the witty and warm-hearted preface by Yves Meyer.
A full list of the 63 papers in the volume can be found here in the Table of Contents*. Jean-Pierre Kahane continues to publish, and the full list of his scientific works at the end of this volume will be updated at each reprinting.
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