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Fourier Transforms in the Complex Domain

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Softcover ISBN: 978-0-8218-1019-4
Product Code: COLL/19
List Price: $61.00 MAA Member Price:$54.90
AMS Member Price: $48.80 Electronic ISBN: 978-1-4704-3167-9 Product Code: COLL/19.E List Price:$57.00
MAA Member Price: $51.30 AMS Member Price:$45.60
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List Price: $91.50 MAA Member Price:$82.35
AMS Member Price: $73.20 Click above image for expanded view Fourier Transforms in the Complex Domain Available Formats:  Softcover ISBN: 978-0-8218-1019-4 Product Code: COLL/19  List Price:$61.00 MAA Member Price: $54.90 AMS Member Price:$48.80
 Electronic ISBN: 978-1-4704-3167-9 Product Code: COLL/19.E
 List Price: $57.00 MAA Member Price:$51.30 AMS Member Price: $45.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$91.50 MAA Member Price: $82.35 AMS Member Price:$73.20
• Book Details

Colloquium Publications
Volume: 191934; 183 pp
MSC: Primary 42;

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.

• Chapters
• Introduction
• Chapter I. Quasi-analytic functions
• Chapter II. Szász’s theorem
• Chapter III. Certain integral expansions
• Chapter IV. A class of singular integral equations
• Chapter V. Entire functions of the exponential type
• Chapter VI. The closure of sets of complex exponential functions
• Chapter VII. Non-harmonic Fourier series and a gap theorem
• Chapter VIII. Generalized harmonic analysis in the complex domain
• Chapter IX. Random functions
• Chapter IX. The harmonic analysis of random functions
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Volume: 191934; 183 pp
MSC: Primary 42;

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.

• Chapters
• Introduction
• Chapter I. Quasi-analytic functions
• Chapter II. Szász’s theorem
• Chapter III. Certain integral expansions
• Chapter IV. A class of singular integral equations
• Chapter V. Entire functions of the exponential type
• Chapter VI. The closure of sets of complex exponential functions
• Chapter VII. Non-harmonic Fourier series and a gap theorem
• Chapter VIII. Generalized harmonic analysis in the complex domain
• Chapter IX. Random functions
• Chapter IX. The harmonic analysis of random functions
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