ON UNIFORM COMPLEX APPROXIMATION BY LACUNARY POLYNOMIALS

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.