On -reflection of harmonic functions and -approximation by harmonic polynomials

DOI10.1070/SM9295zbMath1456.31006MaRDI QIDQ5135759

Konstantin Yu. Fedorovskiy, Peter V. Paramonov

Publication date: 23 November 2020

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

zbMATH Keywords

Poisson operatorharmonic reflection operatorLipschitz-Hölder spacessimple Carathéodory domain\(C^m\)-approximation by harmonic polynomials

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Approximation in the complex plane (30E10) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Boundary value problems in the complex plane (30E25)

Cites Work

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• A reflection result for harmonic functions which vanish on a cylindrical surface
• Harmonic reflection in quasicircles and well-posedness of a Riemann-Hilbert problem on quasidisks
• Remarks on the reflection principle for harmonic functions
• The Schwarz reflection principle for harmonic functions in \(\mathbb R^2\) subject to the Robin condition
• \(C^ m\) approximation by solutions of elliptic equations, and Calderón-Zygmund operators
• Reflection principles for harmonic and polyharmonic functions
• On point to point reflection of harmonic functions across real-analytic hypersurfaces in \(\mathbb{R}^ n\)
• On \(\mathrm{Lip}^m\)-reflection of harmonic functions over boundaries of simple Carathéodory domains
• Extremal barriers on cones with Phragmén-Lindelöf theorems and other applications
• On reflection of harmonic functions in surfaces of revolution
• The Integrability of Superharmonic Functions on Lipschitz Domains
• $ C^m$-APPROXIMATIONS BY HARMONIC POLYNOMIALS ON COMPACT SETS IN $ \mathbb{R}^n$
• Conditions for $ C^m$-approximability of functions by solutions of elliptic equations

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