On \(k\)-regular functions with values in a universal Clifford algebra

DOI10.1016/j.jmaa.2005.06.053zbMath1096.30045OpenAlexW1970040860MaRDI QIDQ819662

Zhong Xiang Zhang

Publication date: 29 March 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.06.053

zbMATH Keywords

Cauchy formulaClifford analysisk-regular functionregular polynomial, Taylor expansion

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) Power series (including lacunary series) in one complex variable (30B10) Polynomials and rational functions of one complex variable (30C10)

Related Items (17)

A representation of sl(2;C) on clifford algebra of even dimension ⋮ The Schwarz lemma for functions with values in \(C(V_{n,0})\) ⋮ The Schwarz type lemma in upper half space in Clifford analysis ⋮ A fourth-order elliptic Riemann type problem in \(\mathbb{R}^{3}\) ⋮ Some properties of operators in Clifford analysis ⋮ On \(k\)-analytic functions of an octonionic variable ⋮ 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 ⋮ Boundary value problems with higher order Lipschitz boundary data for polymonogenic functions in fractal domains ⋮ The Schwarz lemma in Clifford analysis ⋮ Riemann boundary value problem for harmonic functions in Clifford analysis ⋮ A laurent expansion and residue theorems of k-regular functions in clifford analysis ⋮ Some integral representations and singular integral over plane in Clifford analysis ⋮ Some Riemann boundary value problems in Clifford analysis ⋮ Some Riemann boundary value problems in Clifford analysis (I) ⋮ Differential operators, their fundamental solutions and related integral representations in Clifford analysis

Cites Work

• Iterated integral operators in Clifford analysis
• On Cauchy-Pompeiu formula for functions with values in a universal Clifford algebra.
• On regular-analytic functions with values in a Clifford-algebra
• On the singularities of functions with values in a Clifford algebra
• Integral Representation Formulas in Polydomains
• Hyperholomorphic Functions and Second Order Partial Differential Equations in R n
• Hypercomplex Function Theory and Hilbert Modules with Reproducing Kernel
• 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
• Cauchy-Green Type Formulae in Clifford Analysis
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