Abstract:
Results are established on uniform approximation of functions that are continuous on compact subsets of the complex plane and holomorphic in their interiors, by lacunary polynomials whose gaps are of zero or positive density. These generalize and sharpen previous results in this direction by N. U. Arakelyan and the author. Results similar to the Walsh–Lebesgue theorem are given for lacunary polynomials, as well as an inequality for a majorant of the coefficients of the approximating polynomials.
Bibliography: 19 titles.
This publication is cited in the following 6 articles:
T. Gharibyan, W. Luh, J. Müller, “A lacunary version of Mergelian’s approximation theorem”, Journal of Approximation Theory, 162:4 (2010), 709
Martirosyan V.A. Mkrtchyan S.E., “On Mean Approximation by Polynomials with Gaps on Non-Caratheodory Domains”, J. Contemp. Math. Anal.-Armen. Aca., 45:3 (2010), 162–169
Martirosian V.A., Mkrtchyan S.E., “On Mean Approximation by Polynomials with Gaps on Caratheodory Sets”, J. Contemp. Math. Anal.-Armen. Aca., 43:6 (2008), 372–376
Valeri A. Martirosian, Jürgen Müller, “A Liouville-type result for lacunary power series and converse results for universal holomorphic functions”, Analysis, 26:3 (2007), 393
Valeri A. Martirosian, Jürgen Müller, “A Liouville-type result for lacunary power series and converse results for universal holomorphic functions”, Analysis, 26:3 (2006)
Wolfgang Luh, Valeri A. Martirosian, Jürgen Müller, “Universal entire functions with gap power series”, Indagationes Mathematicae, 9:4 (1998), 529
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