The discrete Borel-Pompeiu formula on a rectangular lattice

DOI10.1007/s00006-018-0887-2zbMath1394.39005OpenAlexW2810140096WikidataQ129645478 ScholiaQ129645478MaRDI QIDQ1668611

Anastasiia Legatiuk, Klaus Gürlebeck, Angela Hommel

Publication date: 29 August 2018

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-018-0887-2

zbMATH Keywords

fundamental solutionfinite differencesCauchy-Riemann operatorBorel-Pompeiu formuladiscrete function theory

Mathematics Subject Classification ID

Discrete version of topics in analysis (39A12) Discrete potential theory (31C20) Difference equations in the complex domain (39A45) Discrete analytic functions (30G25)

Related Items (1)

Discrete Hardy spaces for bounded domains in \(\mathbb{R}^n\)

Cites Work

• Discrete Hardy spaces
• On finite difference Dirac operators and their fundamental solutions
• New discretization of complex analysis: the Euclidean and hyperbolic planes
• Basic properties of discrete analytic functions
• Discrete Dirac operators in Clifford analysis
• Method of Difference Potentials and Its Applications
• Application of Holomorphic Functions in Two and Higher Dimensions
• A Basic Framework for Discrete Clifford Analysis
• On finite difference potentials and their applications in a discrete function theory
• Discrete function theory based on skew Weyl relations
• Discrete Clifford Analysis: A Germ of Function Theory
• Linear and nonlinear theories of discrete analytic functions. Integrable structure and isomonodromic Green’s function
• Difference potentials for the Navier–Stokes equations in unbounded domains
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