Deriving harmonic functions in higher dimensional spaces

DOI10.4171/ZAA/1145zbMath1052.30055OpenAlexW1974576704MaRDI QIDQ1876013

Tao Qian, Fransiscus Sommen

Publication date: 6 September 2004

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/1145

zbMATH Keywords

Fourier multiplierssingular integralsharmonic functionsClifford monogenic functions

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Function spaces arising in harmonic analysis (42B35) Functions of hypercomplex variables and generalized variables (30G35) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05)

Related Items (18)

Biaxial monogenic functions from Funk‐Hecke's formula combined with Fueter's theorem ⋮ On the inversion of Fueter's theorem ⋮ Fueter's theorem: the saga continues ⋮ Shifted Appell sequences in Clifford analysis ⋮ Clifford algebra approach to pointwise convergence of Fourier series on spheres ⋮ Cauchy-Kowalevski extensions and monogenic plane waves using spherical monogenics ⋮ Uniform generalizations of Fueter's theorem ⋮ The Fueter primitive of biaxially monogenic functions ⋮ Generating functions of orthogonal polynomials in higher dimensions ⋮ Cauchy-Kowalevski extensions and monogenic plane waves in Clifford analysis ⋮ A new integral formula for the inverse Fueter mapping theorem ⋮ Slice Regular Functions on Regular Quadratic Cones of Real Alternative Algebras ⋮ Fueter's theorem for monogenic functions in biaxial symmetric domains ⋮ Implementing zonal harmonics with the Fueter principle ⋮ On boundary behavior of the Cauchy type integrals with values in a universal Clifford algebra ⋮ Recent Developments for Regular Functions of a Hypercomplex Variable ⋮ Monogenic Gaussian distribution in closed form and the Gaussian fundamental solution ⋮ An alternative proof of Fueter's theorem

Cites Work

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• Generalization of Fueter's result to \(\mathbb{R}^{n+1}\)
• Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space
• Die Funktionentheorie der Differentialgleichungen \(\Delta u=0\) und \(\Delta\Delta u=0\) mit vier reellen Variablen
• The Quaternion Calculus
• On a generalization of Fueter's theorem
• Fourier analysis on starlike Lipschitz surfaces

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