Analytic Functionals on the Sphere (Translations of Mathematical Monographs)
By: Mitsuo Morimoto (editor)Hardback
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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.
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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- ID: 9780821805855
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