The convergence of sequences of rational functions of best approximation. III

Author:
J. L. Walsh

Journal:
Trans. Amer. Math. Soc. **130** (1968), 167-183

MSC:
Primary 30.70

DOI:
https://doi.org/10.1090/S0002-9947-1968-0218590-7

MathSciNet review:
0218590

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References | Similar Articles | Additional Information

**[1]**J. L. Walsh,*Note on the convergence of approximating rational functions of prescribed type*, Proc. Nat. Acad. Sci. U.S.A.**50**(1963), 791–794. MR**0157163****[2]**J. L. Walsh,*The convergence of sequences of rational functions of best approximation*, Math. Ann.**155**(1964), 252–264. MR**0164185**, https://doi.org/10.1007/BF01344163**[3]**J. L. Walsh,*The convergence of sequences of rational functions of best approximation. II*, Trans. Amer. Math. Soc.**116**(1965), 227–237. MR**0188684**, https://doi.org/10.1090/S0002-9947-1965-0188684-0**[4]**J. L. Walsh,*The convergence of sequences of rational functions of best approximation with some free poles*, Approximation of Functions (Proc. Sympos. General Motors Res. Lab., 1964 ), Elsevier Publ. Co., Amsterdam, 1965, pp. 1–16. MR**0186986****[5]**-,*Interpolation and approximation*, Colloq. Publ., Vol. 20, Amer. Math. Soc., Providence, R. I., 1935.**[6]**Joseph L. Walsh,*An extension of the generalized Bernstein lemma*, Colloq. Math.**16**(1967), 91–92. MR**0216009**, https://doi.org/10.4064/cm-16-1-91-92**[7]**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****[8]**J. L. Walsh,*Degree of polynomial approximation to an analytic function as measured by a surface integral*, Proc. Nat. Acad. Sci. U.S.A.**48**(1962), 26–32. MR**0132331****[9]**J. L. Walsh and H. G. Russell,*Integrated continuity conditions and degree of approximation by polynomials or by bounded analytic functions*, Trans. Amer. Math. Soc.**92**(1959), 355–370. MR**0108595**, https://doi.org/10.1090/S0002-9947-1959-0108595-3**[10]**Dunham Jackson,*On certain problems of approximation in the complex domain*, Bull. Amer. Math. Soc.**36**(1930), no. 12, 851–857. MR**1562068**, https://doi.org/10.1090/S0002-9904-1930-05078-8**[11]**H. Margaret Elliott,*On approximation to functions satisfying a generalized continuity condition*, Trans. Amer. Math. Soc.**71**(1951), 1–23. MR**0044627**, https://doi.org/10.1090/S0002-9947-1951-0044627-1**[12]**A. A. Gončar,*On series of rational functions*, Dokl. Akad. Nauk SSSR**143**(1962), 1246–1249 (Russian). MR**0136896****[13]**D. J. Newman,*Rational approximation to |𝑥|*, Michigan Math. J.**11**(1964), 11–14. MR**0171113**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1968-0218590-7

Article copyright:
© Copyright 1968
American Mathematical Society