Best uniform approximation by meromorphic functions with free poles

Poreda, S. J.

doi:10.1090/S0002-9939-1974-0333198-9

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Best uniform approximation by meromorphic functions with free poles
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by S. J. Poreda

Proc. Amer. Math. Soc. 42 (1974), 513-516

DOI: https://doi.org/10.1090/S0002-9939-1974-0333198-9

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Abstract:

Using some recent results on best polynomial approximations, a method for explicitly calculating the meromorphic function with a fixed number of free poles of best uniform approximation to certain functions on a closed Jordan curve is obtained.

References

S. J. Poreda, On the convergence of best uniform deviations, Trans. Amer. Math. Soc. 174 (1973), 49–59. MR 320332, DOI 10.1090/S0002-9947-1973-0320332-3
S. J. Poreda, A characterization of badly approximable functions, Trans. Amer. Math. Soc. 169 (1972), 249–256. MR 306510, DOI 10.1090/S0002-9947-1972-0306510-7