References
Al'per, S. Ya.: On uniform approximations of functions of a complex variable on closed sets. Izvestija Akad. Nauk, SSSR. Ser. mat.19, 423–444 (1955) (Russian)
Dzyadyk, V. K.: On the application of generalized Faber polynomials to the approximation of Cauchy-type integrals and functions of classesA' in domains with a smooth and piecewise-smooth boundary. Ukrain. math. J.24, 3–19 (1972) Translation, pp. 1–14
Gaier, D.: Estimates of conformal mappings near the boundary. Indiana Univ. Math. J.21, 581–595 (1972)
Kövari, T.: On the order of polynomial approximation for closed Jordan domains, J. Approximation Theory,5, 362–373 (1972)
Kövari, T., Pommerenke, Ch.: On Faber polynomials and Faber expansions. Math. Z.99, 193–203 (1967)
Lorentz, G. G.: Approximation of Functions. Athena Series, New York-Chicago-San Francisco: Holt, Rinehart and Winston 1966
Mergelyan, S. N.: Some problems on constructive function theory (Russian). Trudy mat. Inst. Steklov37 (1951)
Mergelyan, S. N.: Uniform approximations of functions of a complex variable. Uspehi mat. Nauk7, 31–122 (1952) (Amer. Math. Soc. Translat. I. Ser.3; 294–391)
Pommerenke, Ch.: Über die Faberschen Polynome schlichter Funktionen. Math. Z.85, 197–208 (1964)
Suetin, P. K.: Fundamental propertes of Faber polynomials. Uspehi mat. Nauk,19, No. 4 (118), 125–154 (1964). Translation: Russ. math. Surveys19, 121–149 (1964)
Walsh, J. L., Elliott, H. M.: Degree of approximation on a Jordan curve. Prov. nat. Acad. Sci., USA38, 1058–1066 (1952)
Warschawski, S. E.: On the differentiability at the boundary in conformal mapping. Proc. Amer. math. Soc.12, 614–620 (1961)
Warschawski, S. E.: On the Hölder continuity at the boundary in conformal maps. J. Math. Mech.18, 423–428 (1968)
Zygmund, A.: Trigonometric Series, 2nd Edition, Vol. 1 Cambridge: Cambridge University Press 1959
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lesley, F.D., Vinge, V.S. & Warschawski, S.E. Approximation by faber polynomials for a class of Jordan domains. Math Z 138, 225–237 (1974). https://doi.org/10.1007/BF01237121
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01237121