A Hermitian Cauchy formula on a domain with fractal boundary

DOI10.1016/j.jmaa.2010.03.032zbMath1201.30060OpenAlexW2028521495MaRDI QIDQ982594

Juan Bory-Reyes, Fred Brackx, Ricardo Abreu-Blaya, Hennie De Schepper, Fransiscus Sommen

Publication date: 7 July 2010

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

Full work available at URL: https://biblio.ugent.be/publication/945416

zbMATH Keywords

Cauchy integralfractal geometryHermitian Clifford analysis

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35)

Related Items (7)

A Cauchy transform for polymonogenic functions on fractal domains ⋮ A Hilbert transform for matrix functions on fractal domains ⋮ Cauchy integral formulae in quaternionic Hermitean Clifford analysis ⋮ Hölder norm estimate for a Hilbert transform in Hermitean Clifford analysis ⋮ Boundary value problems for Dirac operators and Maxwell's equations in fractal domains ⋮ Boundary value problems associated to a Hermitian Helmholtz equation ⋮ Boundary value problems on fractal hypersurfaces for the quaternionic Hermitian system in \(\mathbb R^{4n}\)

Cites Work

• On fundamental solutions in Clifford analysis
• On Cauchy and Martinelli-Bochner integral formulae in Hermitean Clifford analysis
• A matrix Hilbert transform in Hermitean Clifford analysis
• A boundary value problem for Hermitian monogenic functions
• Hermitean Téodorescu transform decomposition of continuous matrix functions on fractal hypersurfaces
• The Howe dual pair in Hermitean Clifford analysis
• Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces
• The Hermitian Clifford analysis toolbox
• The Gauss-Green theorem for fractal boundaries
• Hermitian decomposition of continuous functions on a fractal surface
• Fundaments of Hermitean Clifford analysis. I: Complex structure
• A theoretical framework for wavelet analysis in a Hermitean Clifford setting
• The Realization of small Distances in Plane Sets of Positive Measure
• Complexified clifford analysis
• Hermitian Clifford analysis and resolutions
• Fundaments of Hermitean Clifford analysis part II: splitting ofh-monogenic equations
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