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Uniform Approximation by Entire Functions That Are All Bounded on a Given Set

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Constructive Approximation Aims and scope

Abstract.

For two closed sets F and G in the complex plane C, G \(\neq\) C , we solve the following problem Under what conditions on F and G can every function f , continuous on F and analytic in its interior, be uniformly approximated by entire functions, each of which is bounded on G ?

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Authors and Affiliations

  1. Department of Mathematics (Chair 806), Moscow Aviation Institute, 4, Volokolamskoe Shosse, 125871 Moscow, Russia, RUSSIA

    A. A. Danielyan

  2. Institute of Mathematics of the National, Academy of Sciences of Armenia, American University of Armenia, ARMENIA

    L. A. Rubel

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  1. A. A. Danielyan
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  2. L. A. Rubel
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February 7, 1995. Date revised: October 31, 1995.

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Danielyan, A., Rubel, L. Uniform Approximation by Entire Functions That Are All Bounded on a Given Set. Constr. Approx. 14, 469–473 (1998). https://doi.org/10.1007/s003659900085

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  • DOI: https://doi.org/10.1007/s003659900085

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