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]**D. Jackson,*On certain problems of approximation in the complex domain*, Bull. Amer. Math. Soc.**36**(1930), 851. MR**1562068****[2]**W. E. Sewell,*Degree of approximation by polynomials in the complex domain*, Ann. of Math. Studies, No. 9, Princeton Univ. Press, Princeton, N. J., 1942. MR**0007054 (4:78c)****[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. MR**0213584 (35:4444)****[4]**-,*Approximation by polynomials*:*uniform convergence as implied by mean convergence*, Proc. Nat. Acad. Sci. U.S.A.**55**(1966), 20-25. MR**0188453 (32:5891)****[5]**-,*Interpolation and approximation*, Amer. Math. Soc. Colloq. Publ., Vol. 20, Amer. Math. Soc., Providence, R. I., 1935.**[6]**-,*Approximation by bounded analytic functions*, Mémor. Sci. Math., Fasc. 144, Gauthier-Villars, Paris, 1960. MR**0119001 (22:9770)****[7]**-,*Thé convergence of sequences of rational functions of best approximation with some free poles*, Proc. Sympos. Approximation of Functions, General Motors Corp. (Detroit, 1964), edited by H. L. Garabedian, Elsevier, Amsterdam, 1965, pp. 1-16. MR**0186986 (32:4441)**

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

Article copyright:
© Copyright 1969
American Mathematical Society