Cauchy-Kowalevski extensions and monogenic plane waves using spherical monogenics

DOI10.1007/S00574-013-0016-8zbMath1273.30040OpenAlexW2083676378MaRDI QIDQ360233

Fransiscus Sommen, Nele De Schepper

Publication date: 26 August 2013

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1854/LU-4284286

zbMATH Keywords

Clifford analysisCauchy-Riemann equationaxial monogenic functionbiaxial monogenic functionCK-extensionmonogenic plane waves

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Classical hypergeometric functions, ({}_2F_1) (33C05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (11)

The inverse Fueter mapping theorem for axially monogenic functions of degree \(k\) ⋮ On the inversion of Fueter's theorem ⋮ Uniform generalizations of Fueter's theorem ⋮ The Fueter-Sce mapping and the Clifford–Appell polynomials ⋮ Coherent state transforms and the Weyl equation in Clifford analysis ⋮ On the connection between the Fueter-Sce-Qian theorem and the generalized CK-extension ⋮ Fischer Decomposition and Cauchy–Kovalevskaya Extension in Fractional Clifford Analysis: The Riemann–Liouville Case ⋮ Clifford coherent state transforms on spheres ⋮ Generalized Cauchy-Kovalevskaya extension and plane wave decompositions in superspace ⋮ Extending coherent state transforms to Clifford analysis ⋮ Cauchy-Kovalevskaya extension theorem in fractional Clifford analysis

Cites Work

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• Special functions in Clifford analysis and axial symmetry
• Deriving harmonic functions in higher dimensional spaces
• Cauchy-Kowalevski extensions and monogenic plane waves in Clifford analysis
• The inverse Fueter mapping theorem in integral form using spherical monogenics
• An alternative proof of Fueter's theorem
• Clifford analysis, biaxial symmetry and pseudoanalytic functions
• Monogenic Gaussian distribution in closed form and the Gaussian fundamental solution
• A product and an exponential function in hypercomplex function theory

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