On the degree of polynomial approximation to analytic functions: problem $\beta$
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 by J. L. Walsh and W. E. Sewell PDF
 Trans. Amer. Math. Soc. 49 (1941), 229257 Request permission
References

Bernstein, S. 1926. Leçons sur les Propriétés Extrémales et la Meilleure Approximation des Fonctions Analytiques d’une Variable Réelle, Paris.
 John Curtiss, Interpolation in regularly distributed points, Trans. Amer. Math. Soc. 38 (1935), no. 3, 458–473. MR 1501821, DOI 10.1090/S00029947193515018219
 J. H. Curtiss, A note on the degree of polynomial approximation, Bull. Amer. Math. Soc. 42 (1936), no. 12, 873–878. MR 1563457, DOI 10.1090/S000299041936064554 Faber, G. 1920. Über Tchebyscheffsche Polynome, Journal für die reine und angewandte Mathematik, vol. 150, pp. 79106.
 G. H. Hardy and J. E. Littlewood, A convergence criterion for Fourier series, Math. Z. 28 (1928), no. 1, 612–634. MR 1544980, DOI 10.1007/BF01181186 —1932. Some properties of fractional integrals, ibid., vol. 34, pp. 403439. —1935. An inequality, ibid., vol. 40, pp. 140.
 Freidrich Riesz, Über die Randwerte einer analytischen Funktion, Math. Z. 18 (1923), no. 1, 87–95 (German). MR 1544621, DOI 10.1007/BF01192397
 W. E. Sewell, Generalized derivatives and approximation by polynomials, Trans. Amer. Math. Soc. 41 (1937), no. 1, 84–123. MR 1501892, DOI 10.1090/S00029947193715018921 Szegö, G. 1939. Orthogonal Polynomials, American Mathematical Society Colloquium Publications, vol. 23. de la vallée Poussin, Ch. J. 1914. Cours d’Analyse, vol. 1, Paris. —1919. Leçons sur l’Approximation des Fonctions d’une Variable Réelle, Paris.
 J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587
 J. L. Walsh and W. E. Sewell, Note on the relation between continuity and degree of polynomial approximation in the complex domain, Bull. Amer. Math. Soc. 43 (1937), no. 8, 557–563. MR 1563586, DOI 10.1090/S000299041937066031
 J. L. Walsh and W. E. Sewell, Note on degree of trigonometric and polynomial approximation to an analytic function, Bull. Amer. Math. Soc. 44 (1938), no. 12, 865–873. MR 1563892, DOI 10.1090/S000299041938068930
 J. L. Walsh and W. E. Sewell, Sufficient conditions for various degrees of approximation by polynomials, Duke Math. J. 6 (1940), 658–705. MR 2592, DOI 10.1215/S0012709440006512
 J. L. Walsh and W. E. Sewell, Note on degree of trigonometric and polynomial approximation to an analytic function, in the sense of least $p$th powers, Bull. Amer. Math. Soc. 46 (1940), 312–319. MR 1863, DOI 10.1090/S000299041940072106
Additional Information
 © Copyright 1941 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 49 (1941), 229257
 MSC: Primary 30.0X
 DOI: https://doi.org/10.1090/S0002994719410003818X
 MathSciNet review: 0003818