Abstract
Let G be a simply-connected domain in the plane with rectifiable boundary, γ be a rectifiable Jordan curve in G. The paper is devoted to estimates of the Kolmogorov widths of the unit ball of the space EP(G) in the space Lq(γ).
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Literature cited
G. M. Goluzin, Geometric Theory of Functions of a Complex Variable [in Russian], Moscow (1966).
V. D. Erokhin, “Best linear approximation of functions which can be extended analytically from a given continuous to a given domain,” Usp. Mat. Nauk,23, No. 1, 91–132 (1968).
V. P. Zakharyuta and N. I. Skiba, “Estimates of n-widths of certain classes of functions, analytic on Riemann surfaces,” Mat. Zametki,19, No. 6, 899–913 (1976).
O. G. Parfenov, “Asymptotics of singular numbers of inclusion operators of some classes of analytic functions,” Mat. Sb.,4(8), 632–641 (1981).
P. K. Suetin, “Polynomials, orthogonal with respect to area, and Bieberbach polynomials,” Tr. Mat. Inst. Akad. Nauk SSSR,100 (1971).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 108–112, 1984.
The author thanks M. Z. Solomyak for help with this paper.
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Parfenov, O.G. Faber polynomials and widths of Smirnov classes in the integral metric. J Math Sci 31, 2706–2708 (1985). https://doi.org/10.1007/BF02107255
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DOI: https://doi.org/10.1007/BF02107255