ON AE CONVERGENCE OF DURRMEYER-STIELTJES POLYNOMIALS

[摘要] Let nu be a finite Borel measure on [0, 1]. We introduce the notation of the Durrmeyer-Stieltjes polynomials [GRAPHICS] where [GRAPHICS] are the basic Bernstein polynomials. We prove that the maximal operator of the sequence (D-n) is of weak type and the sequence of polynomials (D-n nu) converges a.e. on [0, 1] to the absolutely continuous part of nu. (C) 1994 Academic Press, Inc.

[发布日期] 1994-10-01