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On weighted approximation by lacunary polynomials on the rays emerging from the origin. (English) Zbl 1199.30026
Authors’ abstract: We obtain a necessary and sufficient condition for the lacunary polynomials to be dense in weighted Banach spaces of functions on the rays emerging from the origin. This generalizes the solution to the classical Bernstein problem given by T. Hall [Cong. Math. Scand. 1938, 367-369 (1938; JFM 65.0249.03)] and S. Izumi and T. Kawats [Tohoku Math. J. 43, 267–273 (1937; Zbl 0017.31203)].
MSC:
30B60 Completeness problems, closure of a system of functions of one complex variable
41A10 Approximation by polynomials
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