APPLICATIONS OF BERNSTEIN-DURRMEYER OPERATORS IN ESTIMATING THE COVERING NUMBER  

作　　者：Chunping Zhang Jianli Wang Baohuai Sheng 

机构地区：[1]Zhejiang Industry Polytechnic College, China [2]Shaoxing College of Arts and Sciences, China

出　　处：《Analysis in Theory and Applications》2010年第2期186-200,共15页分析理论与应用（英文刊）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 10871226)

摘　　要：The paper deals with estimates of the covering number for some Mercer kernel Hilbert space with Bernstein-Durrmeyer operators. We first give estimates of l2- norm of Mercer kernel matrices reproducing by the kernelsK（α,β）（x,y）：=∑∞k=0 Ck（α,β）（x）Qk（α,β）（y）,where Qk（α,β） （x） are the Jacobi polynomials of order k on （0, 1 ）, Ck（α,β） 〉 0 are real numbers, and from which give the lower and upper bounds of the covering number for some particular reproducing kernel Hilbert space reproduced by Kα,β （x, y）.The paper deals with estimates of the covering number for some Mercer kernel Hilbert space with Bernstein-Durrmeyer operators. We first give estimates of l2- norm of Mercer kernel matrices reproducing by the kernelsK（α,β）（x,y）：=∑∞k=0 Ck（α,β）（x）Qk（α,β）（y）,where Qk（α,β） （x） are the Jacobi polynomials of order k on （0, 1 ）, Ck（α,β） 〉 0 are real numbers, and from which give the lower and upper bounds of the covering number for some particular reproducing kernel Hilbert space reproduced by Kα,β （x, y）.

关 键 词：Mercer kernel matrix covering number Bernstein-Durrmeyer operator 

分 类 号：O174.41[理学—数学] O174.14[理学—基础数学]