Best constants for tensor products of Bernstein type operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:301

Article

de la Cal, J ; Cárcamo, J

关键词: best constant;    Bernstein-type operators;    tensor product;    gamma operators;    beta operators;    Baskakov operators;    modulus of continuity;    gamma distribution;    beta distribution;    negative binomial distribution;    Poisson process;    gamma process;   

DOI  :  10.1016/j.jmaa.2004.06.064

来源: Elsevier

【 摘 要 】

For the tensor product of k copies of the same one-dimensional Bernstein-type operator L, we consider the problem of finding the best constant in preservation of the usual modulus of continuity for the l(p)-norm on R-k. Two main results are obtained: the first one gives both necessary and sufficient conditions in order that 1 + k(1-1/p) is the best uniform constant for a single operator; the second one gives sufficient conditions in order that I + k(1-1/p) is the best uniform constant for a family of operators. The general results are applied to several classical families of operators usually considered in approximation theory. Throughout the paper, probabilistic concepts and methods play an important role. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free