Uniform approximation by solutions of elliptic equations
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- by Barnet M. Weinstock PDF
- Proc. Amer. Math. Soc. 41 (1973), 513-517 Request permission
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
- Andrew Browder, Introduction to function algebras, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0246125
- Felix E. Browder, Approximation by solutions of partial differential equations, Amer. J. Math. 84 (1962), 134–160. MR 178247, DOI 10.2307/2372809
- Felix E. Browder, Functional analysis and partial differential equations. II, Math. Ann. 145 (1961/62), 81–226. MR 136857, DOI 10.1007/BF01342796 L. Hörmander, Linear partial differential operators, Die Grundlehren der math. Wissenschaften, Band 116, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #4221.
- Fritz John, Plane waves and spherical means applied to partial differential equations, Interscience Publishers, New York-London, 1955. MR 0075429
- Eva Kallin, A nonlocal function algebra, Proc. Nat. Acad. Sci. U.S.A. 49 (1963), 821–824. MR 152907, DOI 10.1073/pnas.49.6.821
- Barnet M. Weinstock, Approximation by holomorphic functions on certain product sets in $C^{n}$, Pacific J. Math. 43 (1972), 811–822. MR 344523
Additional 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