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On the degree of complex rational approximation to real functions

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Abstract

Iff∈C[−1, 1] is real-valued, letE mnR (f) andE mnC (f) be the errors in best approximation tof in the supremum norm by rational functions of type (m, n) with real and complex coefficients, respectively. We show that form≥n−1≥0

$$\gamma _{mn} = \inf \{ {{E_{mn}^C (f)} \mathord{\left/ {\vphantom {{E_{mn}^C (f)} {E_{mn}^R (f)}}} \right. \kern-\nulldelimiterspace} {E_{mn}^R (f)}}:f \in C[ - 1,1]\} = \tfrac{1}{2}.$$

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Authors and Affiliations

  1. Department of Mathematics, Everyman's University, 16 Klausner Street, POB 39328, Tel-Aviv, Israel

    A. L. Levin

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  1. A. L. Levin
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Communicated by Edward B. Saff.

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Levin, A.L. On the degree of complex rational approximation to real functions. Constr. Approx 2, 213–219 (1986). https://doi.org/10.1007/BF01893427

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  • DOI: https://doi.org/10.1007/BF01893427

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