A necessary and sufficient condition for uniform approximation by certain rational modules
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- by J. J. Carmona Doménech
- Proc. Amer. Math. Soc. 86 (1982), 487-490
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671221-7
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Abstract:
Let $X$ be a compact subset of ${\mathbf {C}}$ with empty interior and let $g$ be a complex function of class ${C^2}$ in a neighborhood of $X$. For $Z = \left \{ {z \in X|\partial g(z)/\partial \bar z = 0} \right \}$, we prove that $R(X) + gR(X)$ is uniformly dense in $C(X)$ if and only if $R(Z) = C(Z)$.References
- Andrew Browder, Introduction to function algebras, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0246125
- Robert B. Burckel, An introduction to classical complex analysis. Vol. 1, Pure and Applied Mathematics, vol. 82, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. MR 555733, DOI 10.1007/978-3-0348-9374-9
- Anthony G. O’Farrell, Annihilators of rational modules, J. Functional Analysis 19 (1975), no. 4, 373–389. MR 0380428, DOI 10.1016/0022-1236(75)90063-4
- Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
- Tavan Trent and James Li Ming Wang, Uniform approximation by rational modules on nowhere dense sets, Proc. Amer. Math. Soc. 81 (1981), no. 1, 62–64. MR 589136, DOI 10.1090/S0002-9939-1981-0589136-0
- James Li Ming Wang, Approximation by rational modules on nowhere dense sets, Pacific J. Math. 80 (1979), no. 1, 293–295. MR 534719, DOI 10.2140/pjm.1979.80.293
- Lawrence Zalcmann, Analytic capacity and rational approximation, Lecture Notes in Mathematics, No. 50, Springer-Verlag, Berlin-New York, 1968. MR 0227434, DOI 10.1007/BFb0070657
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 487-490
- MSC: Primary 30E10; Secondary 46J10
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671221-7
- MathSciNet review: 671221