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Two spaces of generalized functions based on harmonic polynomials

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Polynômes Orthogonaux et Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1171))

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Abstract

Two spaces of generalized functions on the unit sphere Ωq−1 ⊂ ℝq are introduced. Both types of generalized functions can be identified with suitable classes of harmonic functions. They are projective and inductive limits of Hilbert spaces. Several natural classes of continuous and continuously extendible operators are discussed: Multipliers, differentiations, harmonic contractions/expansions and harmonic shifts. The latter two classes of operators are "parametrized" by the full affine semigroup ℝn.

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References

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Authors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, the Netherlands

    J. de Graaf

Authors
  1. J. de Graaf
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Editor information

Claude Brezinski André Draux Alphonse P. Magnus Pascal Maroni André Ronveaux

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© 1985 Springer-Verlag

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de Graaf, J. (1985). Two spaces of generalized functions based on harmonic polynomials. In: Brezinski, C., Draux, A., Magnus, A.P., Maroni, P., Ronveaux, A. (eds) Polynômes Orthogonaux et Applications. Lecture Notes in Mathematics, vol 1171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076541

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  • DOI: https://doi.org/10.1007/BFb0076541

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16059-5

  • Online ISBN: 978-3-540-39743-4

  • eBook Packages: Springer Book Archive

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