Uniform approximation by solutions of elliptic equations
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- by Barnet M. Weinstock
- Proc. Amer. Math. Soc. 41 (1973), 513-517
- DOI: https://doi.org/10.1090/S0002-9939-1973-0340794-0
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Abstract:
The space ${H_A}(K)$ of continuous functions on a compact set $K$ in Euclidean space which can be uniformly approximated by solutions of the elliptic, constant-coefficient partial differential equation $Af = 0$ is studied. In particular, it is shown that ${H_A}(K)$ is local, in the same sense as in the theory of rational approximation in the complex plane. Simultaneous approximation of functions and their derivatives is also considered.References
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 513-517
- MSC: Primary 35E99; Secondary 35J30, 46J10
- DOI: https://doi.org/10.1090/S0002-9939-1973-0340794-0
- MathSciNet review: 0340794