Duality for harmonic differential forms via Clifford analysis

Ricardo Abreu-Blaya; Juan Bory-Reyes; Richard Delanghe; Frank Sommen

doi:10.1007/s00006-007-0034-y

Duality for harmonic differential forms via Clifford analysis

Ricardo Abreu-Blaya, Juan Bory-Reyes, Richard Delanghe, Frank Sommen

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The space HF _k (Ω) of harmonic multi-vector fields in a domain Ω ⊂ ℝⁿ as introduced in [1] is closely connected to the space of harmonic forms. The main aim of this paper is to characterize the dual space of HF _k (E) being E ⊂ ℝⁿ a compact set. It is proved that HF _k (E) ^* is isomorphic to a certain quotient space of so-called harmonic pairs outside E vanishing at infinity.

Original language	English
Pages (from-to)	589-610
Number of pages	22
Journal	Advances in Applied Clifford Algebras
Volume	17
Issue number	4
DOIs	https://doi.org/10.1007/s00006-007-0034-y
State	Published - Oct 2007
Externally published	Yes

Keywords

Clifford analysis
Harmonic differential forms
Multivector fields

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title = "Duality for harmonic differential forms via Clifford analysis",

abstract = "The space HF k (Ω) of harmonic multi-vector fields in a domain Ω ⊂ ℝn as introduced in [1] is closely connected to the space of harmonic forms. The main aim of this paper is to characterize the dual space of HF k (E) being E ⊂ ℝn a compact set. It is proved that HF k (E) * is isomorphic to a certain quotient space of so-called harmonic pairs outside E vanishing at infinity.",

keywords = "Clifford analysis, Harmonic differential forms, Multivector fields",

author = "Ricardo Abreu-Blaya and Juan Bory-Reyes and Richard Delanghe and Frank Sommen",

note = "Funding Information: Research of the third author was supported by the FWO Research Network WO. 003. 01N, research of the fourth author was supported by the FWO “Krediet aan Navorsers: 1.5.106.02”",

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T1 - Duality for harmonic differential forms via Clifford analysis

AU - Abreu-Blaya, Ricardo

AU - Bory-Reyes, Juan

AU - Delanghe, Richard

AU - Sommen, Frank

N1 - Funding Information: Research of the third author was supported by the FWO Research Network WO. 003. 01N, research of the fourth author was supported by the FWO “Krediet aan Navorsers: 1.5.106.02”

PY - 2007/10

Y1 - 2007/10

N2 - The space HF k (Ω) of harmonic multi-vector fields in a domain Ω ⊂ ℝn as introduced in [1] is closely connected to the space of harmonic forms. The main aim of this paper is to characterize the dual space of HF k (E) being E ⊂ ℝn a compact set. It is proved that HF k (E) * is isomorphic to a certain quotient space of so-called harmonic pairs outside E vanishing at infinity.

AB - The space HF k (Ω) of harmonic multi-vector fields in a domain Ω ⊂ ℝn as introduced in [1] is closely connected to the space of harmonic forms. The main aim of this paper is to characterize the dual space of HF k (E) being E ⊂ ℝn a compact set. It is proved that HF k (E) * is isomorphic to a certain quotient space of so-called harmonic pairs outside E vanishing at infinity.

KW - Clifford analysis

KW - Harmonic differential forms

KW - Multivector fields

UR - http://www.scopus.com/inward/record.url?scp=35148841411&partnerID=8YFLogxK

U2 - 10.1007/s00006-007-0034-y

DO - 10.1007/s00006-007-0034-y

M3 - Artículo

SN - 0188-7009

VL - 17

SP - 589

EP - 610

JO - Advances in Applied Clifford Algebras

JF - Advances in Applied Clifford Algebras

IS - 4

ER -

Duality for harmonic differential forms via Clifford analysis

Abstract

Keywords

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