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Product Code:  MMONO/178 
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Hardcover ISBN:  9780821805855 
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Product Code:  MMONO/178.B 
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Hardcover ISBN:  9780821805855 
Product Code:  MMONO/178 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445935 
Product Code:  MMONO/178.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821805855 
eBook ISBN:  9781470445935 
Product Code:  MMONO/178.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 178; 1998; 160 ppMSC: Primary 46; Secondary 32; 58
This book treats spherical harmonic expansion of real analytic functions and hyperfunctions on the sphere. Because a onedimensional sphere is a circle, the simplest example of the theory is that of Fourier series of periodic functions.
The author first introduces a system of complex neighborhoods of the sphere by means of the Lie norm. He then studies holomorphic functions and analytic functionals on the complex sphere. In the onedimensional case, this corresponds to the study of holomorphic functions and analytic functionals on the annular set in the complex plane, relying on the Laurent series expansion. In this volume, it is shown that the same idea still works in a higherdimensional sphere. The FourierBorel transformation of analytic functionals on the sphere is also examined; the eigenfunction of the Laplacian can be studied in this way.
ReadershipGraduate students, research mathematicians and mathematical physicists working in analysis.

Table of Contents

Chapters

Fourier expansion of hyperfunctions on the circle

Spherical harmonic expansion of functions on the sphere

Harmonic functions on the Lie ball

Holomorphic functions on the complex sphere

Holomorphic functions on the Lie ball

Entire functions of exponential type

FourierBorel transformation on the complex sphere

Spherical FourierBorel transformation on the Lie ball


Reviews

This book is written in a clear and lucid style and its layout is excellent. The book can be recommended to the wide audience of researchers and students interested in theory of hyperfunctions and harmonic analysis.
Zentralblatt MATH


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This book treats spherical harmonic expansion of real analytic functions and hyperfunctions on the sphere. Because a onedimensional sphere is a circle, the simplest example of the theory is that of Fourier series of periodic functions.
The author first introduces a system of complex neighborhoods of the sphere by means of the Lie norm. He then studies holomorphic functions and analytic functionals on the complex sphere. In the onedimensional case, this corresponds to the study of holomorphic functions and analytic functionals on the annular set in the complex plane, relying on the Laurent series expansion. In this volume, it is shown that the same idea still works in a higherdimensional sphere. The FourierBorel transformation of analytic functionals on the sphere is also examined; the eigenfunction of the Laplacian can be studied in this way.
Graduate students, research mathematicians and mathematical physicists working in analysis.

Chapters

Fourier expansion of hyperfunctions on the circle

Spherical harmonic expansion of functions on the sphere

Harmonic functions on the Lie ball

Holomorphic functions on the complex sphere

Holomorphic functions on the Lie ball

Entire functions of exponential type

FourierBorel transformation on the complex sphere

Spherical FourierBorel transformation on the Lie ball

This book is written in a clear and lucid style and its layout is excellent. The book can be recommended to the wide audience of researchers and students interested in theory of hyperfunctions and harmonic analysis.
Zentralblatt MATH