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titchmarsh e introduction theory fourier int 2ed 1962

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Textbook in PDF format The object of this book is to give a more systematic account of the elements of the theory of Fourier integrals than has hitherto been given. I have, however, not attempted to deal with a number of important topics of recent growth: Wiener’s Tauberian theorems; applications to almost periodic functions, quasi-analytic functions, and integral functions; Stieltjes integrals; harmonic analysis in general; and Bochner’s generalized integrals, and the theory for functions of several variables, of which an account is given in Bochner’s book. The reader requires only a general knowledge of analysis, though he will presumably be familiar with the elements of the theory of Fourier series. The book may be read as a sequel to my Theory of Functions. A great variety of applications of Fourier integrals are to be found in the literature, often in the form of ‘operators’, and often in the works of authors who are evidently not specially interested in analysis. As exercises in the theory I have written out a few of these applications as it seemed to me that an analyst should. I have retained, as having a certain picturesqueness, some references to ‘ heat ’, ‘ radiation ’, and so forth; but the interest is purely analytical, and the reader need not know whether such things exist

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titchmarsh e introduction theory fourier int 2ed 1962