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 & Appl.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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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

Originele taal-2	Engels
Titel	Polynômes Ortogonaux et Applications (Proceedings of the Laguerre Symposium, Bar-le-Duc, France, October 15-18, 1984)
Redacteuren	C. Brezinski, A. Draux, A.P. Magnus
Plaats van productie	Berlin
Uitgeverij	Springer
Pagina's	164-173
Aantal pagina's	10
ISBN van elektronische versie	978-3-540-39743-4
ISBN van geprinte versie	978-3-540-16059-5
DOI's	https://doi.org/10.1007/BFb0076541
Status	Gepubliceerd - 1985

Publicatie series

Naam	Lecture Notes in Mathematics
Volume	1171
ISSN van geprinte versie	0075-8434

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@inproceedings{fba9075f4538497eb4f20e9009987d09,

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.",

year = "1985",

doi = "10.1007/BFb0076541",

language = "English",

isbn = "978-3-540-16059-5",

series = "Lecture Notes in Mathematics",

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)",

address = "Germany",

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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). uitgave / C. Brezinski; A. Draux; A.P. Magnus. Berlin: Springer, 1985. blz. 164-173 (Lecture Notes in Mathematics; Vol. 1171).

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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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

U2 - 10.1007/BFb0076541

DO - 10.1007/BFb0076541

M3 - Conference contribution

SN - 978-3-540-16059-5

T3 - Lecture Notes in Mathematics

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EP - 173

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

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A2 - Draux, A.

A2 - Magnus, A.P.

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Two spaces of generalized functions based on harmonic polynomials

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