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Transactions of the American Mathematical Society

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On the row convergence of the Walsh array for meromorphic functions.


Author: E. B. Saff
Journal: Trans. Amer. Math. Soc. 146 (1969), 241-257
MSC: Primary 30.70
MathSciNet review: 0265608
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  • [2] 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, 10.1007/BF01170632
  • [3] -, ``The convergence of sequences of rational functions of best approximation with some free poles,'' Approximation of functions, H. L. Garabedian, Editor, Elsevier, Amsterdam, 1965.
  • [4] R. de Montessus, Sur les fractions continues algébriques, Bull. Soc. Math. France 30 (1902), 28–36 (French). MR 1504403
  • [5] E. B. Saff, Polynomials of interpolation and approximation to meromorphic functions, Trans. Amer. Math. Soc. 143 (1969), 509–522. MR 0252656, 10.1090/S0002-9947-1969-0252656-1
  • [6] R. Wilson, Divergent continued fractions and polar singularities, Proc. London Math. Soc. 26 (1927), 159-168.
  • [7] -, Divergent continued fractions and polar singularities. II, Proc. London Math. Soc. 27 (1928), 497-512.
  • [8] -, Divergent continued fractions and polar singularities. III, Proc. London Math. Soc. 28 (1928), 128-145.
  • [9] J. L. Walsh, A sequence of rational functions with application to approximation by bounded analytic functions, Duke Math. J. 30 (1963), 177–189. MR 0171929
  • [10] O. Perron, Die Lehre von den Kettenbrüchen, 2nd ed., Teubner, Leipzig, 1929.
  • [11] J. L. Walsh, Surplus free poles of approximating rational functions, Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 896–901. MR 0173774

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DOI: https://doi.org/10.1090/S0002-9947-1969-0265608-2
Article copyright: © Copyright 1969 American Mathematical Society