Differential operators, their fundamental solutions and related integral representations in Clifford analysis

DOI10.1080/17476930500481327zbMath1184.30042OpenAlexW1998833848MaRDI QIDQ3423503

Heinz Otto, Zhong Xiang Zhang, Heinrich Begehr

Publication date: 14 February 2007

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476930500481327

zbMATH Keywords

fundamental solutionsDirac operatorsHelmholtz operatorClifford analysisCauchy-Pompeiu representations

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Functions of hypercomplex variables and generalized variables (30G35) Fundamental solutions to PDEs (35A08) Integral representations of solutions to PDEs (35C15) PDEs in connection with quantum mechanics (35Q40) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Research exposition (monographs, survey articles) pertaining to functions of a complex variable (30-02) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

Related Items (5)

Integral Representations Related to Complex Partial Differential Operators ⋮ Dirichlet-type problems for n-Poisson equation in Clifford analysis ⋮ Integral representations for hyperbolic harmonic function in the clifford algebra Cl_n+1,0 ⋮ Dirichlet problem for inhomogeneous biharmonic equation in Clifford analysis ⋮ Cauchy-type integral formula and Plemelj formula of hypermonogenic functions on unbounded domains

Cites Work

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• On regular-analytic functions with values in a Clifford-algebra
• On the singularities of functions with values in a Clifford algebra
• Hyperkomplexe Differentiale
• Integral Representation Formulas in Polydomains
• Hyperholomorphic Functions and Second Order Partial Differential Equations in R n
• Analysis and Applications of Holomorphic Functions in Higher Dimensions
• A Cauchy's Integral Formula for Functions with Values in a Universal Clifford Algebra and its Applications
• Integral representations in quaternionic analysis related to the helmholtz operator
• Cauchy-Green Type Formulae in Clifford Analysis

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