ACTA issues

Approximation by lacunary Bernstein and self-reciprocal polynomials

A. Kroó, J. Szabados

Acta Sci. Math. (Szeged) 60:3-4(1995), 467-486

Abstract. Continuing the investigation of Müntz type problems for Bernstein polynomials $x^{k_j}(1-x)^{n-k_j}$ started in [3], we introduce the notion of density of the sequence $\{k_j\} $, and prove convergence theorems when this density is at least $1/2$. A particular borderline-case ($k_j=2j$) is reformulated and solved in terms of self-reciprocal polynomials, whose approximation theoretic properties are of independent interest. Approximation by positive linear combinations of the above mentioned Bernstein polynomials is also considered.

AMS Subject Classification (1991): 41A10, 41A17, 41A29

Received April 29, 1994. (Registered under 5645/2009.)