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Mergelyan sets and the modulus of continuity of analytic functions. (English) Zbl 0313.30036


MSC:

30E10 Approximation in the complex plane

References:

[1] Beurling, A., Études sur un Problème de Majoration (1933), Almquist and Wiksell: Almquist and Wiksell Upsala · JFM 59.1042.03
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[3] Fuchs, W. H.J, Théorie de l’approximation des fonctions d’une variable complexe, (Seminaire de Mathématiques Supérieures. Seminaire de Mathématiques Supérieures, Été 1967 (1968), Les Presses de l’Université de Montréal: Les Presses de l’Université de Montréal Montréal) · Zbl 0199.39701
[4] Hardy, G. H.; Littlewood, J. E., Some properties of fractional integrals. II, Math. Zeit., 34, 403-439 (1931) · Zbl 0003.15601
[5] Rubel, L. A.; Shields, A. L.; Taylor, B. A., Mergelyan sets and the modulus of continuity, (Lorentz, G. G., Approximation Theory (1973), Academic Press: Academic Press New York) · Zbl 0317.30037
[6] Rudin, W., Function Theory in Polydiscs (1969), Benjamin: Benjamin New York · Zbl 0177.34101
[7] Sewell, W. E., Degree of Approximation by Polynomials in the Complex Domain (1942), Princeton University Press: Princeton University Press Princeton · Zbl 0063.08342
[8] A. Stray; A. Stray · Zbl 0257.30038
[9] Tamrazov, P. M., Contour and solid structure properties of holomorphic functions of a complex variable, Russ. Math. Surveys, 28, 141-173 (1973) · Zbl 0273.30036
[10] Tamrazov, P. M., Solid inverse theorems of polynomial approximation for regular compacta in the complex plane, Sov. Math. Dokl., 12, 855-858 (1971) · Zbl 0234.30033
[11] Tamrazov, P. M., Constructive and structural properties of functions on compacta of the complex plane, (All-Union Conference on the Theory of Functions of a Complex Variable. All-Union Conference on the Theory of Functions of a Complex Variable, Khar’kov. All-Union Conference on the Theory of Functions of a Complex Variable. All-Union Conference on the Theory of Functions of a Complex Variable, Khar’kov, Abstracts of Papers (1971)), 206-208 · Zbl 0212.42101
[12] Tamrazov, P. M., Boundary and solid properties of holomorphic functions in a complex domain, Dokl. Acad. Nauk., 204, 565-568 (1972) · Zbl 0256.30035
[13] Titchmarsh, E. C., The Theory of Functions (1949), Oxford University Press: Oxford University Press New York · Zbl 0035.18001
[14] Zygmund, A., (Trigonometric Series, Vol. I (1959), Cambridge University Press: Cambridge University Press New York) · JFM 58.0280.01
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