On the row convergence of the Walsh array for meromorphic functions.
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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 —, “The convergence of sequences of rational functions of best approximation with some free poles,” Approximation of functions, H. L. Garabedian, Editor, Elsevier, Amsterdam, 1965.
- R. de Montessus, Sur les fractions continues algébriques, Bull. Soc. Math. France 30 (1902), 28–36 (French). MR 1504403
- E. B. Saff, Polynomials of interpolation and approximation to meromorphic functions, Trans. Amer. Math. Soc. 143 (1969), 509–522. MR 252656, DOI 10.1090/S0002-9947-1969-0252656-1 R. Wilson, Divergent continued fractions and polar singularities, Proc. London Math. Soc. 26 (1927), 159-168. —, Divergent continued fractions and polar singularities. II, Proc. London Math. Soc. 27 (1928), 497-512. —, Divergent continued fractions and polar singularities. III, Proc. London Math. Soc. 28 (1928), 128-145.
- J. L. Walsh, A sequence of rational functions with application to approximation by bounded analytic functions, Duke Math. J. 30 (1963), 177–189. MR 171929 O. Perron, Die Lehre von den Kettenbrüchen, 2nd ed., Teubner, Leipzig, 1929.
- J. L. Walsh, Surplus free poles of approximating rational functions, Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 896–901. MR 173774, DOI 10.1073/pnas.52.4.896
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 146 (1969), 241-257
- MSC: Primary 30.70
- DOI: https://doi.org/10.1090/S0002-9947-1969-0265608-2
- MathSciNet review: 0265608