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Analytic Functionals on the Sphere
Mitsuo Morimoto, International Christian University, Tokyo, Japan
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Translations of Mathematical Monographs
1998; 160 pp; hardcover
Volume: 178
ISBN-10: 0-8218-0585-1
ISBN-13: 978-0-8218-0585-5
List Price: US$86
Member Price: US$68.80
Order Code: MMONO/178
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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.

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

Table of Contents

  • 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
  • Fourier-Borel transformation on the complex sphere
  • Spherical Fourier-Borel transformation on the Lie ball
  • Bibliography
  • Index
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