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)


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.


Heat Kernel Heat Function Dimensional Vector Space Dimensional Sphere Spherical Harmonic Expansion 
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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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