On Cauchy-Pompeiu formula for functions with values in a universal Clifford algebra.

DOI10.1016/S0252-9602(17)30150-9zbMath1145.30314OpenAlexW960865780MaRDI QIDQ1871518

Heinrich Begehr, Jinyuan Du, Zhong Xiang Zhang

Publication date: 24 September 2003

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0252-9602(17)30150-9

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) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Series solutions to PDEs (35C10)

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On \(k\)-regular functions with values in a universal Clifford algebra ⋮ Dirichlet-type problems for n-Poisson equation in Clifford analysis ⋮ Generalized Cauchy theorem in Clifford analysis and boundary value problems for regular functions ⋮ New versions of the Plemelj-Sochocki formula in Clifford analysis ⋮ Generalized integral representations for functions with values in \(C(V_{3,3})\) ⋮ Riemann boundary value problems for triharmonic functions in Clifford analysis ⋮ Dirichlet problem for inhomogeneous biharmonic equation in Clifford analysis ⋮ Cauchy integral formula on the distinguished boundary with values in complex universal Clifford algebra ⋮ Riemann boundary value problem for harmonic functions in Clifford analysis ⋮ On boundary behavior of the Cauchy type integrals with values in a universal Clifford algebra ⋮ A laurent expansion and residue theorems of k-regular functions in clifford analysis ⋮ Plemelj formula for Cauchy type integral on certain distinguished boundary in universal Clifford analysis ⋮ Some integral representations and singular integral over plane in Clifford analysis ⋮ Higher order Borel-Pompeiu representations in Clifford analysis ⋮ Some Riemann boundary value problems in Clifford analysis

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