Book by Wiener, Norbert

2013 Reprint of 1958 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. A series of lectures on the role of nonlinear processes in physics, mathematics, electrical engineering, physiology, and communication theory. From the preface: "For some time I have been interested in a group of phenomena depending upon random processes. One the one hand, I have recorded the random shot effect as a suitable input for testing nonlinear circuits. On the other hand, for some of the work that Professor W. A. Rosenblith and I have been doing concerning the nature of the electroencephalogram, and in particular of the alpha rhythm, it has occurred to me to use the model of a system of random nonlinear oscillators excited by a random input. . . . At the beginning we had contemplated a series of only four or five lectures. My ideas developed pari passu with the course, and by the end of the term we found ourselves with a set of fifteen lectures. The last few of these were devoted to the application of my ideas to problems in the statistical mechanics of gases. This work is both new and tentative, and I found that I had to supplement my course by the writing over of these with the help of Professer Y. W. Lee. "

2014 Reprint of 1959 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. 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. This book contains Wiener's essential ideas regarding harmonic analysis and should be read by anyone working in the field.