Cauchy’s Formula in Clifford Analysis: An Overview

DOI10.1007/978-3-030-23854-4_1zbMath1461.30114OpenAlexW2980658435MaRDI QIDQ5115029

Vladimír Souček, Hennie De Schepper, Roman Lávička, Fred Brackx

Publication date: 29 June 2020

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-23854-4_1

zbMATH Keywords

Dirac operatorClifford algebraClifford analysismonogenic functionsCauchy's formulaquaternionic monogenicityhermitian monogenicity

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels) (32A26) Monogenic and polygenic functions of one complex variable (30A05)

Cites Work

• Cauchy integral formulae in quaternionic Hermitean Clifford analysis
• Fischer decomposition in symplectic harmonic analysis
• On Cauchy and Martinelli-Bochner integral formulae in Hermitean Clifford analysis
• Quaternionic Clifford analysis: the Hermitian setting
• The Hermitian Clifford analysis toolbox
• Fundaments of Hermitean Clifford analysis. I: Complex structure
• Fundaments of quaternionic Clifford analysis. I: Quaternionic structure
• Fischer decomposition for osp(4|2)-monogenics in quaternionic Clifford analysis
• Quaternionic Hermitian spinor systems and compatibility conditions
• Irreducible (m)-modules of Hermitean monogenics
• Fundaments of Hermitean Clifford analysis part II: splitting ofh-monogenic equations
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