Analytic Functionals on the Sphere
Book Details
Format
Hardback or Cased Book
Book Series
Translations of Mathematical Monographs
ISBN-10
0821805851
ISBN-13
9780821805855
Publisher
American Mathematical Society
Imprint
American Mathematical Society
Country of Manufacture
US
Country of Publication
GB
Publication Date
Sep 30th, 1998
Print length
170 Pages
Weight
539 grams
Ksh 25,400.00
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Introduces a system of complex neighborhoods of the sphere by means of the Lie norm. This book treats spherical harmonic expansion of real analytic functions and hyper functions on the sphere. It studies holomorphic functions and analytic functionals on the complex sphere.
This book treats spherical harmonic expansion of real analytic functions and hyper functions 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.
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