On the convergence of best uniform deviations
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- by S. J. Poreda PDF
- Trans. Amer. Math. Soc. 179 (1973), 49-59 Request permission
Abstract:
If a function f is continuous on a closed Jordan curve $\Gamma$ and meromorphic inside $\Gamma$, then the polynomials of best uniform approximation to f on $\Gamma$ converge interior to $\Gamma$. Furthermore, the limit function can in each case be explicitly determined in terms of the mapping function for the interior of $\Gamma$. Applications and generalizations of this result are also given.References
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C. Carathéodory and L. Fejér, Rend. Circ. Mat. Palermo 32 (1911), 218-239.
- G. M. Goluzin, Geometric theory of functions of a complex variable, Translations of Mathematical Monographs, Vol. 26, American Mathematical Society, Providence, R.I., 1969. MR 0247039, DOI 10.1090/mmono/026
- A. I. Markushevich, Theory of functions of a complex variable. Vol. I, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. Translated and edited by Richard A. Silverman. MR 0171899
- Günter Meinardus, Approximation of functions: Theory and numerical methods, Expanded translation of the German edition, Springer Tracts in Natural Philosophy, Vol. 13, Springer-Verlag New York, Inc., New York, 1967. Translated by Larry L. Schumaker. MR 0217482, DOI 10.1007/978-3-642-85643-3
- S. J. Poreda, Estimates for best approximation to rational functions, Trans. Amer. Math. Soc. 159 (1971), 129–135. MR 291475, DOI 10.1090/S0002-9947-1971-0291475-6
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 179 (1973), 49-59
- MSC: Primary 30A82
- DOI: https://doi.org/10.1090/S0002-9947-1973-0320332-3
- MathSciNet review: 0320332