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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Best uniform approximation by solutions of elliptic differential equations
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by P. M. Gauthier and D. Zwick PDF
Trans. Amer. Math. Soc. 342 (1994), 359-374 Request permission


We investigate best uniform approximations to continuous functions on compact subsets of ${\mathbb {R}^n}$ by solutions of elliptic differential equations and, in particular, by harmonic functions. An axiomatic setting general enough to encompass problems of this kind is given, and in this context we extend necessary and sufficient conditions for best harmonic approximation on precompact Jordan domains to arbitrary compact sets and to more general classes of solutions of linear elliptic differential equations.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 342 (1994), 359-374
  • MSC: Primary 41A50; Secondary 31B99, 35B99
  • DOI:
  • MathSciNet review: 1152322