## 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

AMS Classifications

46F05 46F10 31B05 20G05

Original language | English |
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Title of host publication | Polynômes Ortogonaux et Applications (Proceedings of the Laguerre Symposium, Bar-le-Duc, France, October 15-18, 1984) |

Editors | C. Brezinski, A. Draux, A.P. Magnus |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 164-173 |

Number of pages | 10 |

ISBN (Electronic) | 978-3-540-39743-4 |

ISBN (Print) | 978-3-540-16059-5 |

DOIs | |

Publication status | Published - 1985 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 1171 |

ISSN (Print) | 0075-8434 |