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Title of Journal: Results Math

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Abbravation: Results in Mathematics

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Birkhäuser-Verlag

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10.1007/bf02718009

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1420-9012

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Recent Developments In Harmonic Approximation Wit

Authors: D H Armitage P M Gauthier
Publish Date: 2013/04/17
Volume: 29, Issue: 1-2, Pages: 1-15
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Abstract

A theorem of JL Walsh 1929 says that if E is a compact subset of Rn with connected complement and if u is harmonic on a neighbourhood of E then u can be uniformly approximated on E by functions harmonic on the whole of Rn In Part I of this article we survey some generalizations of Walsh’s theorem from the period 1980–94 In Part II we discuss applications of Walsh’s theorem and its generalizations to four diverse topics universal harmonic functions the Radon transform the maximum principle and the Dirichlet problem

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Other Papers In This Journal:
  1. Attracting and Invariant Sets of Nonlinear Stochastic Neutral Differential Equations with Delays
  2. L p -L q Estimates For Solutions To The Damped Plate Equation In Exterior Domains
  3. Defect and Area in Beltrami–Klein Model of Hyperbolic Geometry
  4. Limits of integrals involving almost periodic functions
  5. Asymptotische LÖsungen Der Translationsgleichung
  6. Representation Formulas of Curves in a Two- and Three-Dimensional Lightlike Cone
  7. Decompositions of para-complex vector bundles and para-complex affine immersions
  8. Smooth Stable Planes
  9. Blaschke Dupin hypersurfaces and equiaffine tubes
  10. Matrix Representations of Sturm–Liouville Problems with Finite Spectrum
  11. On the Variation-Diminishing Property
  12. Real Hypersurfaces in Complex Two-plane Grassmannians with $${\mathfrak{D}^{\bot}}$$-Parallel Shape Operator
  13. Point-Reflection Geometries, Geometric K-Loops and Unitary Geometries
  14. Stability of Two Types of Cubic Fuzzy Set-Valued Functional Equations
  15. Pedal Curves Part I: Homogeneous Differential Equation
  16. Regelflächen von Strahlensystemen Mit Demselben SphÄrischen Bild
  17. On the de la Vallée-Poussin Means on the Sphere
  18. Type $${\mathcal{}}$$ Sets and the ttractors of Infinite Iterated Function Systems
  19. Orthocentric Simplices and Biregularity
  20. Conditions for Starlikeness of Multivalent Functions
  21. Rigidity of Complete Minimal Hypersurfaces in the Euclidean Space
  22. On the Rate of Almost Everywhere Convergence of Abel-Cartwright means on L p ( R n )
  23. A Class of Nonlocal Impulsive Problems for Integrodifferential Equations in Banach Spaces
  24. Minimal Submanifolds in S p+3 with Constant Scalar Curvature
  25. Closed form of the Fourier–Borel Kernel in the Framework of Clifford Analysis
  26. Approximation by Linear Combinations of Complex Phillips Operators in Compact Disks
  27. Liouville Theorems for F -Harmonic Maps and Their Applications
  28. A Theorem on Homogeneous Differential Polynomials
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