On the degree of polynomial approximation to analytic functions: problem 𝛽

On the degree of polynomial approximation to analytic functions: problem $\beta$
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Trans. Amer. Math. Soc. 49 (1941), 229-257

DOI: https://doi.org/10.1090/S0002-9947-1941-0003818-X

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References

Leçons sur les Propriétés Extrémales et la Meilleure Approximation des Fonctions Analytiques d’une Variable Réelle

John Curtiss, Interpolation in regularly distributed points, Trans. Amer. Math. Soc. 38 (1935), no. 3, 458–473. MR 1501821, DOI 10.1090/S0002-9947-1935-1501821-9
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/S0002-9904-1936-06455-4

Über Tchebyscheffsche Polynome

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

Some properties of fractional integrals

An inequality

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/S0002-9947-1937-1501892-1

Orthogonal Polynomials

Cours d’Analyse

Leçons sur l’Approximation des Fonctions d’une Variable Réelle

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/S0002-9904-1937-06603-1
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/S0002-9904-1938-06893-0
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/S0012-7094-40-00651-2
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/S0002-9904-1940-07210-6