Bounded limits of analytic functions
HTML articles powered by AMS MathViewer
- by A. M. Davie PDF
- Proc. Amer. Math. Soc. 32 (1972), 127-133 Request permission
Abstract:
Let U be a bounded open plane set, and let f be a bounded analytic function on U, which is the pointwise limit of a bounded sequence $\{ {f_n}\}$ of uniformly continuous analytic functions. It is shown that one can find another such sequence $\{ {f’_n}\}$, converging to f, and bounded by the supremum norm of f. A similar result is proved for approximation by rational functions.References
- Andrew Browder, Point derivations on function algebras, J. Functional Analysis 1 (1967), 22–27. MR 0211262, DOI 10.1016/0022-1236(67)90024-9
- O. J. Farrell, On approximation by polynomials to a function analytic in a simply connected region, Bull. Amer. Math. Soc. 41 (1935), no. 10, 707–711. MR 1563174, DOI 10.1090/S0002-9904-1935-06182-8
- Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
- L. A. Rubel and A. L. Shields, Bounded approximation by polynomials, Acta Math. 112 (1964), 145–162. MR 174913, DOI 10.1007/BF02391768 B. K. Øksendal, Null sets for annihilating measures for $R(X)$, Amer. J. Math. (to appear).
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 127-133
- MSC: Primary 30A18
- DOI: https://doi.org/10.1090/S0002-9939-1972-0293069-1
- MathSciNet review: 0293069