Numerical null-solutions to iterated Dirac operator on bounded domains

DOI10.1007/s11785-016-0544-5zbMath1366.65092OpenAlexW2290948029WikidataQ58038838 ScholiaQ58038838MaRDI QIDQ523040

Min Ku, Uwe Kaehler

Publication date: 20 April 2017

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-016-0544-5

zbMATH Keywords

convergencenumerical exampleTaylor seriesdiscrete Dirac operatordiscrete Clifford analysisAlmansi-type decompositiondiscrete Euler operatorsnumerical null-solutions

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs in connection with quantum mechanics (35Q40) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items

Plemelj projections in discrete quaternionic analysis, Cauchy-Pompeiu Formula for Discrete Monogenic Functions, Discrete Hardy spaces for bounded domains in \(\mathbb{R}^n\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Riemann boundary value problems for iterated Dirac operator on the ball in Clifford analysis
• Fueter polynomials in discrete Clifford analysis
• Discrete Hardy spaces
• On finite difference Dirac operators and their fundamental solutions
• Basic properties of discrete analytic functions
• Fischer decomposition for difference Dirac operators
• Iterated Dirac operators in \(\mathbb C^ n\)
• Taylor series expansion in discrete Clifford analysis
• Discrete Dirac operators in Clifford analysis
• Further theory of operational calculus on discrete analytic functions
• Discrete Hilbert boundary value problems on half lattices
• Transmission boundary problems for Dirac operators on Lipschitz domains and applications to Maxwell’s and Helmholtz’s equations
• (Discrete) Almansi type decompositions: an umbral calculus framework based on osp(1|2) symmetries
• On Cauchy estimates and growth orders of entire solutions of iterated Dirac and generalized Cauchy–Riemann equations
• A Basic Framework for Discrete Clifford Analysis
• Almansi‐type theorems in Clifford analysis
• On a quaternionic Maxwell equation for the time-dependent electromagnetic field in a chiral medium
• Discrete function theory based on skew Weyl relations
• Discrete Clifford Analysis: A Germ of Function Theory
• Difference potentials for the Navier–Stokes equations in unbounded domains
• Discrete quantum mechanics