Representations of super-holomorphic functions and their applications

DOI10.1080/17476933.2016.1170821zbMath1350.31014OpenAlexW2339123145MaRDI QIDQ2816596

Hongfen Yuan, Valery V. Karachik

Publication date: 25 August 2016

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2016.1170821

zbMATH Keywords

Poisson equationinhomogeneous polyharmonic equationRiquier's problemAlmansi representation

Mathematics Subject Classification ID

Biharmonic and polyharmonic equations and functions in higher dimensions (31B30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Analysis on supermanifolds or graded manifolds (58C50)

Cites Work

• Unnamed Item
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• Riemann boundary value problems for iterated Dirac operator on the ball in Clifford analysis
• Normalized system for the super Laplace operator
• The RH boundary value problem of the \(k\)-monogenic functions
• Iterated Dirac operators in \(\mathbb C^ n\)
• A computation of Green functions for the weighted biharmonic operators \(\Delta| z| ^{-2\alpha}\Delta\), with \(\alpha > -1\)
• Decompositions of \(L^p\) and Hardy spaces of polyharmonic functions
• Correct rules for Clifford calculus on superspace
• On an expansion of Almansi type
• Construction of polynomial solutions to some boundary value problems for Poisson’s equation
• Decomposition ofk-monogenic functions in superspace
• Integration in superspace using distribution theory
• Almansi‐type theorems in Clifford analysis
• Spherical harmonics and integration in superspace
• On solvability conditions for the Neumann problem for a polyharmonic equation in the unit ball

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