Two spaces of generalized functions based on harmonic polynomials

J. Graaf, de

doi:10.1007/BFb0076541

Two spaces of generalized functions based on harmonic polynomials

J. Graaf, de

Center for Analysis, Scientific Computing and Applications

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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 language	English
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	https://doi.org/10.1007/BFb0076541
Publication status	Published - 1985

Publication series

Name	Lecture Notes in Mathematics
Volume	1171
ISSN (Print)	0075-8434

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10.1007/BFb0076541

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title = "Two spaces of generalized functions based on harmonic polynomials",

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 Classifications46F05 46F10 31B05 20G05 ",

author = "{Graaf, de}, J.",

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publisher = "Springer",

pages = "164--173",

editor = "C. Brezinski and A. Draux and A.P. Magnus",

booktitle = "Polyn{\^o}mes Ortogonaux et Applications (Proceedings of the Laguerre Symposium, Bar-le-Duc, France, October 15-18, 1984)",

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Two spaces of generalized functions based on harmonic polynomials. / Graaf, de, J.
Polynômes Ortogonaux et Applications (Proceedings of the Laguerre Symposium, Bar-le-Duc, France, October 15-18, 1984). ed. / C. Brezinski; A. Draux; A.P. Magnus. Berlin: Springer, 1985. p. 164-173 (Lecture Notes in Mathematics; Vol. 1171).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

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N2 - 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 Classifications46F05 46F10 31B05 20G05

AB - 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 Classifications46F05 46F10 31B05 20G05

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DO - 10.1007/BFb0076541

M3 - Conference contribution

SN - 978-3-540-16059-5

T3 - Lecture Notes in Mathematics

SP - 164

EP - 173

BT - Polynômes Ortogonaux et Applications (Proceedings of the Laguerre Symposium, Bar-le-Duc, France, October 15-18, 1984)

A2 - Brezinski, C.

A2 - Draux, A.

A2 - Magnus, A.P.

PB - Springer

CY - Berlin

ER -

Two spaces of generalized functions based on harmonic polynomials

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