**Translations of Mathematical Monographs**

1998;
160 pp;
Hardcover

MSC: Primary 46;
Secondary 32; 58

**Print ISBN: 978-0-8218-0585-5
Product Code: MMONO/178**

List Price: $91.00

Individual Member Price: $72.80

# Analytic Functionals on the Sphere

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*Mitsuo Morimoto*

This book treats spherical harmonic expansion of real analytic functions and
hyperfunctions on the sphere. Because a one-dimensional 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 one-dimensional 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
higher-dimensional sphere. The Fourier-Borel transformation of analytic
functionals on the sphere is also examined; the eigenfunction of the Laplacian
can be studied in this way.

#### Table of Contents

# Table of Contents

## Analytic Functionals on the Sphere

#### Readership

Graduate students, research mathematicians and mathematical physicists working in analysis.

#### 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