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A Characterization of Analytic Functionals on the Sphere II

  • Mitsuo Morimoto
  • Masanori Suwa
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 8)

Abstract

Matsuzawa [4] started to characterize generalized functions (for example, distributions or hyperfunctions) on ℝn as initial values of heat functions. His idea is valid even for quasi-analytic ultradistri- butions in \( \varepsilon {{'}_{{\left\{ s \right\}}}}\left( {{{\mathbb{R}}^{n}}} \right) \) with s > 1/2. Note that functions in ε{s}(ℝn)are non-quasi-analytic if s > 1 but quasi-analytic if s ≤ 1. We propose a method to extend Matuzawa’s idea for wider range of s.

In the first part [7] we studied generalized functions on the one- dimensional sphere (that is, the circle). We study here generalized functions on the n-dimensional sphere \( {\mathbb{S}^n} \) with n > 1, expanding them into the spherical harmonic functions.

Keywords

Heat Kernel Heat Function Dimensional Vector Space Dimensional Sphere Spherical Harmonic Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Mitsuo Morimoto
    • 1
  • Masanori Suwa
    • 2
  1. 1.Department of MathematicsInternational Christian UniversityTokyoJapan
  2. 2.Department of MathematicsSophia UniversityTokyoJapan

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