Two spaces of generalized functions based on harmonic polynomials

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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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