**Colloquium Publications**

Volume: 19;
1934;
183 pp;
Softcover

MSC: Primary 42;

**Print ISBN: 978-0-8218-1019-4
Product Code: COLL/19**

List Price: $61.00

AMS Member Price: $48.80

MAA Member Price: $54.90

**Electronic ISBN: 978-1-4704-3167-9
Product Code: COLL/19.E**

List Price: $57.00

AMS Member Price: $45.60

MAA Member Price: $51.30

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# Fourier Transforms in the Complex Domain

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*N. Wiener; R. C. Paley*

With the aid of Fourier-Mellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasi-analytic functions, Mercer's theorem on summability, Milne's integral equation of radiative equilibrium, the theorems of Münz and Szász concerning the closure of sets of powers of an argument, Titchmarsh's theory of entire functions of semi-exponential type with real negative zeros, trigonometric interpolation and developments in polynomials of the form \(\sum^N_1A_ne^{i\lambda_nx}\), lacunary series, generalized harmonic analysis in the complex domain, the zeros of random functions, and many others.

#### Table of Contents

# Table of Contents

## Fourier Transforms in the Complex Domain

- Cover Cover11
- Title page i2
- Frontispiece iii4
- Dedication v6
- Preface vii8
- Contents ix10
- Introduction 112
- Chapter I. Quasi-analytic functions 1425
- Chapter II. Szász’s theorem 2637
- Chapter III. Certain integral expansions 3748
- Chapter IV. A class of singular integral equations 4960
- Chapter V. Entire functions of the exponential type 6879
- Chapter VI. The closure of sets of complex exponential functions 8697
- Chapter VII. Non-harmonic Fourier series and a gap theorem 100111
- Chapter VIII. Generalized harmonic analysis in the complex domain 128139
- Chapter IX. Random functions 140151
- Chapter IX. The harmonic analysis of random functions 163174
- Bibliography 179190
- Index 183194
- Back Cover Back Cover1196