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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References | Similar Articles | Additional Information

**[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