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Analyse mathématique --- Mathematical analysis --- TRANSFORMATION DE FOURIER --- THEOREMES TAUBERIENS --- INTEGRALE DE FOURIER --- ANALYSE HARMONIQUE
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Sciences --- Comportement humain. --- Cybernétique. --- Aspect social.
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Fourier, Séries de --- Théorèmes taubériens --- Analyse harmonique
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Systèmes, Théorie des --- Systèmes non-linéaires --- Quantum theory.
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The book was written from lectures given at the University of Cambridge and maintains throughout a high level of rigour whilst remaining a highly readable and lucid account. Topics covered include the Planchard theory of the existence of Fourier transforms of a function of L2 and Tauberian theorems. The influence of G. H. Hardy is apparent from the presence of an application of the theory to the prime number theorems of Hadamard and de la Vallee Poussin. Both pure and applied mathematicians will welcome the reissue of this classic work. For this reissue, Professor Kahane's Foreword briefly describes the genesis of Wiener's work and its later significance to harmonic analysis and Brownian motion.
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It has been the opinion of many that Wiener will be remembered for his Extrapolation long after Cybernetics is forgotten. Indeed few computer-science students would know today what cybernetics is all about, while every communication student knows what Wiener's filter is. The work was circulated as a classified memorandum in 1942, as it was connected with sensitive war-time efforts to improve radar communication. This book became the basis for modern communication theory, by a scientist considered one of the founders of the field of artificial intelligence. Combining ideas from statistics and time-series analysis, Wiener used Gauss's method of shaping the characteristic of a detector to allow for the maximal recognition of signals in the presence of noise. This method came to be known as the "Wiener filter.".
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