Recent developments in harmonic approximation, with applications

DOI10.1007/BF03322201zbMath0859.31001MaRDI QIDQ1911973

David H. Armitage, Paul M. Gauthier

Publication date: 7 April 1997

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

zbMATH Keywords

maximum principleDirichlet problemRadon transformuniversal functionsharmonic functionsJFM 55.0889.05tangential harmonic approximation

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Approximation in the complex plane (30E10) Multidimensional problems (41A63) Research exposition (monographs, survey articles) pertaining to approximations and expansions (41-02) Research exposition (monographs, survey articles) pertaining to potential theory (31-02)

Related Items (11)

Universality of holomorphic functions bounded on closed sets ⋮ Universal families and hypercyclic operators ⋮ On a characterization of Arakelian sets ⋮ Chaotic differentiation operators on harmonic functions and simple connectivity ⋮ A dynamical characterization of sub-Arakelian subsets ⋮ Universal holomorphic and harmonic functions with additional properties ⋮ Small entire functions with infinite growth index ⋮ Extended abstract theory of universal series and applications ⋮ Dense-lineability of sets of Birkhoff-universal functions with rapid decay ⋮ Approximation in measure: the Dirichlet problem, universality and the Riemann hypothesis ⋮ Permissible growth rates for Birkhoff type universal harmonic functions

Cites Work

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• The Radon transform
• The Dirichlet problem with non-compact boundary
• Uniform Approximation on Closed Sets by Harmonic Functions with Newtonian Singularities
• A Maximum Principle for Subharmonic and Plurisubharmonic Functions
• Better than Uniform Approximation on Closed Sets by Harmonic Functions with Singularities
• Asymptotic Maximum Principles for Subharmonic and Plurisubharmonic Functions
• Uniform Approximation on Unbounded Sets by Harmonic Functions with Logarithmic Singularities
• Uniqueness and Nonuniqueness for the Radon Transform
• Nonuniqueness for the Radon Transform
• Uniform And Tangential Approximations By Meromorphic Functions on Closed Sets
• Elliptic Partial Differential Equations of Second Order
• Tangential Harmonic Approximation on Relatively Closed Sets

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