Extensions of D. Jackson's theorem on best complex polynomial mean approximations

Authors:
J. L. Walsh and E. B. Saff

Journal:
Trans. Amer. Math. Soc. **138** (1969), 61-69

MSC:
Primary 30.70

DOI:
https://doi.org/10.1090/S0002-9947-1969-0241662-9

MathSciNet review:
0241662

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**[1]**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**[2]**W. E. Sewell,*Degree of Approximation by Polynomials in the Complex Domain*, Annals of Mathematical Studies, no. 9, Princeton University Press, Princeton, N. J., 1942. MR**0007054****[3]**J. L. Walsh,*Approximation by polynomials: Uniform convergence as implied by mean convergence. III*, Proc. Nat. Acad. Sci. U.S.A.**56**(1966), 1406–1408. MR**0213584****[4]**J. L. Walsh,*Approximation by polynomials: Uniform convergence as implied by mean convergence*, Proc. Nat. Acad. Sci. U.S.A.**55**(1966), 20–25. MR**0188453****[5]**-,*Interpolation and approximation*, Amer. Math. Soc. Colloq. Publ., Vol. 20, Amer. Math. Soc., Providence, R. I., 1935.**[6]**J. L. Walsh,*Approximation by bounded analytic functions*, Mémor. Sci. Math., Fasc. 144, Gauthier-Villars, Paris, 1960. MR**0119001****[7]**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**

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DOI:
https://doi.org/10.1090/S0002-9947-1969-0241662-9

Article copyright:
© Copyright 1969
American Mathematical Society