In the present paper, we find that the Bernstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help ...In the present paper, we find that the Bernstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help of the de la Vallée properties of the Bernstein-Durrmeyer operators a sequence of translation network operators is constructed and its degree of approximation is dealt.展开更多
The paper is related to the norm estimate of Mercer kernel matrices. The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on [0, 1] × [0, 1] based on the Bernstein-Durrm...The paper is related to the norm estimate of Mercer kernel matrices. The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on [0, 1] × [0, 1] based on the Bernstein-Durrmeyer operator kernel are obtained, with which and the approximation property of the Bernstein-Durrmeyer operator the lower and upper bounds of the Rayleigh entropy number and the l2 -norm for general Mercer kernel matrices on [0, 1] x [0, 1] are provided.展开更多
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...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）.展开更多
基金Supported by the NSF of P.R.China(10471130)the NSF of Zhejiang Province(Y604003)
文摘In the present paper, we find that the Bernstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help of the de la Vallée properties of the Bernstein-Durrmeyer operators a sequence of translation network operators is constructed and its degree of approximation is dealt.
基金Supported by the Science Foundation of Zhejiang Province(Y604003)
文摘The paper is related to the norm estimate of Mercer kernel matrices. The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on [0, 1] × [0, 1] based on the Bernstein-Durrmeyer operator kernel are obtained, with which and the approximation property of the Bernstein-Durrmeyer operator the lower and upper bounds of the Rayleigh entropy number and the l2 -norm for general Mercer kernel matrices on [0, 1] x [0, 1] are provided.
基金Supported by the National Natural Science Foundation of China (Grant No. 10871226)
文摘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）.
