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Softcover ISBN:  9780821810194 
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Product Code:  COLL/19.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $112.50 $85.50 
AMS Member Price:  $100.00 $76.00 
Softcover ISBN:  9780821810194 
Product Code:  COLL/19 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
eBook ISBN:  9781470431679 
Product Code:  COLL/19.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 
Softcover ISBN:  9780821810194 
eBook ISBN:  9781470431679 
Product Code:  COLL/19.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $112.50 $85.50 
AMS Member Price:  $100.00 $76.00 

Book DetailsColloquium PublicationsVolume: 19; 1934; 183 ppMSC: Primary 42
With the aid of FourierMellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasianalytic 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 semiexponential 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

Chapters

Introduction

Chapter I. Quasianalytic 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. Nonharmonic 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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With the aid of FourierMellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasianalytic 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 semiexponential 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. Quasianalytic 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. Nonharmonic 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