Translations of Mathematical Monographs 1998; 160 pp; hardcover Volume: 178 ISBN10: 0821805851 ISBN13: 9780821805855 List Price: US$86 Member Price: US$68.80 Order Code: MMONO/178
 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. 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
 FourierBorel transformation on the complex sphere
 Spherical FourierBorel transformation on the Lie ball
 Bibliography
 Index
