Uniform rational approximation

Author:
Li Ming Yang

Journal:
Proc. Amer. Math. Soc. **123** (1995), 201-206

MSC:
Primary 30H05; Secondary 30E10, 41A20, 46J10

DOI:
https://doi.org/10.1090/S0002-9939-1995-1242112-7

MathSciNet review:
1242112

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Abstract: Let *K* be a compact subset of the complex plane , and let and be the closures in of polynomials and rational functions with poles off *K*, respectively. Suppose that is a nonpeak point for , and *g* is continuous on and in a neighborhood of . Then is not dense in . In fact, our proof shows that there are a lot of smooth functions which are not in the closure of .

**[B]**A Browder,*Introduction to function algebra*, Benjamin, New York, 1969. MR**0246125 (39:7431)****[G]**T. W. Gamelin,*Uniform algebra*, Prentice-Hall, Englewood Cliffs, NJ, 1969. MR**0410387 (53:14137)****[T]**J. E. Thomson,*Approximation in the mean by polynomials*, Ann. of Math. (2)**133**(1991), 477-507. MR**1109351 (93g:47026)****[T2]**-,*Uniform approximation by rational functions*, Indiana Univ. Math. J.**42**(1993), 167-177. MR**1218711 (94h:41030)**

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DOI:
https://doi.org/10.1090/S0002-9939-1995-1242112-7

Article copyright:
© Copyright 1995
American Mathematical Society