Some examples in degree of approximation by rational functions
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- by D. Aharonov and J. L. Walsh PDF
- Trans. Amer. Math. Soc. 159 (1971), 427-444 Request permission
Abstract:
We exhibit examples of (1) series that converge more rapidly than any geometric series where the function represented has a natural boundary, (2) the convergence of a series with maximum geometric degree of convergence yet having limit points of poles of the series everywhere dense on a circumference in the complement of $E$, (3) a Padé table for an entire function whose diagonal has poles every-where dense in the plane and (4) a corresponding example for the table of rational functions of best approximation of prescribed type.References
- J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587
- J. L. Walsh, On approximation to an analytic function by rational functions of best approximation, Math. Z. 38 (1934), no. 1, 163–176. MR 1545445, DOI 10.1007/BF01170632
- J. L. Walsh, On the overconvergence of certain sequences of rational functions of best approximation, Acta Math. 57 (1931), no. 1, 411–435. MR 1555339, DOI 10.1007/BF02403051 O. Perron, Die Lehre von den Kettenbrüchen, Chelsea, New York, 1929. H. S. Wall, Analytic theory of continued fractions, Chelsea, New York, 1967.
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 159 (1971), 427-444
- MSC: Primary 30.70
- DOI: https://doi.org/10.1090/S0002-9947-1971-0289787-5
- MathSciNet review: 0289787