Abstract
The paper is devoted to a description of a new class of convex domains in ℂn such that an analog of the classical Jackson-Bernstein theorem is valid for domains of this class. Bibliography: 7 titles.
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N. A. Shirokov, “Direct theorem on a strictly convex domain in ℂn,” Zap. Nauchn. Semin. POMI, 206, 151–173 (1993).
N. A. Shirokov, “Jackson-Bernstein theorem in strictly pseudoconvex domains in ℂn,” Constr. Appr., No. 4, 455–461 (1989).
L. A. Aizenberg, “Integral representation of functions that are holomorphic in convex domains of the space ℂn,” Dokl. Akad. Nauk SSSR, 151, 1247–1249 (1963).
E. M. Dynkin, “Smooth function on flat sets,” Dokl. Akad. Nauk SSSR, 208, 25–27 (1973).
I. Stein, Singular Integrals and Differential Properties of Functions [Russian translation], Moscow (1973).
G. M. Henkin and J. Leiterer, Theory of Functions on Complex Manifolds, Akademic-Verlag, Berlin (1984).
V. K. Dzyadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Moscow (1977).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 98–112.
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Shirokov, N.A. Uniform polynomial approximations on convex domains in ℂn . J Math Sci 141, 1564–1572 (2007). https://doi.org/10.1007/s10958-007-0064-y
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DOI: https://doi.org/10.1007/s10958-007-0064-y