Two spaces of generalized functions based on harmonic polynomials

J. Graaf, de

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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.

    AMS Classifications
    46F05 46F10 31B05 20G05
    Original languageEnglish
    Title of host publicationPolynômes Ortogonaux et Applications (Proceedings of the Laguerre Symposium, Bar-le-Duc, France, October 15-18, 1984)
    EditorsC. Brezinski, A. Draux, A.P. Magnus
    Place of PublicationBerlin
    PublisherSpringer
    Pages164-173
    Number of pages10
    ISBN (Electronic)978-3-540-39743-4
    ISBN (Print)978-3-540-16059-5
    DOIs
    Publication statusPublished - 1985

    Publication series

    NameLecture Notes in Mathematics
    Volume1171
    ISSN (Print)0075-8434

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