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Deriving harmonic functions in higher dimensional spaces
T. Qian1; F. Sommen2
2003
Source PublicationJournal for Analysis and its Applications
ISSN0232-2064
Volume22Issue:2Pages:1–12
Abstract

For a harmonic function, by replacing its variables with norms of vectors in some multi-dimensional spaces we may induce a new function in a higher dimensional space. We show that after applying to it a certain power of the Laplacian we obtain a new harmonic function in the higher dimensional space. We show that Poisson and Cauchy kernels and Newton potentials, as well as heat kernels are all deducible using this method based on their forms in the lowest dimensional spaces. Fueter’s Theorem and its generalizations are deducible as well from our results. The latter has been used to singular integral and Fourier multiplier theory on the unit spheres and their Lipschitz perturbations of higher dimensional Euclidean spaces.

KeywordHarmonic Functions Cauchy-riemann Operator Clifford Monogenic Functions Singular Integrals Fourier Multipliers
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000185604700002
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Citation statistics
Cited Times [WOS]:22   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
Corresponding AuthorT. Qian; F. Sommen
Affiliation1.Univ. of Macau, Fac. Sci. & Techn., P.O. Box 3001, Macau
2.Univ. of Ghent, Dept. Math. Anal., Galglaan 2, B-9000 Gent, Belgium
Recommended Citation
GB/T 7714
T. Qian,F. Sommen. Deriving harmonic functions in higher dimensional spaces[J]. Journal for Analysis and its Applications,2003,22(2):1–12.
APA T. Qian,&F. Sommen.(2003).Deriving harmonic functions in higher dimensional spaces.Journal for Analysis and its Applications,22(2),1–12.
MLA T. Qian,et al."Deriving harmonic functions in higher dimensional spaces".Journal for Analysis and its Applications 22.2(2003):1–12.
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