Recent Developments In Harmonic Approximation,With Applications |
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Authors: | D. H. Armitage P. M. Gauthier |
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Affiliation: | 1. Department Of Pure Mathematics, Queen’s University, Belfast BT7 Inn, Northern Ireland 2. Départment De Mathématiques Et De Statistique, Université De Montréal, Montréal, Québec, Canada, H3C 3J7
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Abstract: | A theorem of J.L. 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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