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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
DOI: https://doi.org/10.1090/S0002-9947-1969-0265608-2
MathSciNet review: 0265608
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  • [1] J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, Third edition. American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587
    J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, Fourth edition. American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1965. MR 0218588
  • [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, https://doi.org/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, https://doi.org/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