This paper concerns the problem of the Kolmogorov n-width, the linear re-width, the Gel'fand n-width and the Bernstein re-width of Sobolev classes of the periodic multivariate functions in the space Lp(Td) and the...This paper concerns the problem of the Kolmogorov n-width, the linear re-width, the Gel'fand n-width and the Bernstein re-width of Sobolev classes of the periodic multivariate functions in the space Lp(Td) and the average Bernstein o-width, average Kolmogorov o-widths, the average linear o-widths of Sobolev classes of the multivariate functions in the space LP(R ), where p = (p1,…,pd), 1 < Pj < ∞o, j = 1,2,…,d, or pj = ∞,j = 1,2,…, d. Their weak asymptotic behaviors are established for the corresponding quantities.展开更多
Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of th...Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.展开更多
For β 〉 0 and an integer r 〉 2, denote by H∞,β those 2π-periodic, real-valued functions f on R, which are analytic in Sβ = {z ∈ C： [ImzI 〈β} and satisfy the restriction If（r）（z）[ ≤ 1, z ∈ Sβ. The opt...For β 〉 0 and an integer r 〉 2, denote by H∞,β those 2π-periodic, real-valued functions f on R, which are analytic in Sβ = {z ∈ C： [ImzI 〈β} and satisfy the restriction If（r）（z）[ ≤ 1, z ∈ Sβ. The optimal quadrature formulae about information composed of the values of a function and its kth （k ： 1,..., r - 1） derivatives on free knots for the classes H∞,β are obtained, and the error estimates of the optimal quadrature formulae are exactly determined.展开更多
Ⅰ. INTRODUCTION AND DEFINITIONLet r be a positive integer and p∈[1, +∞]. We consider the following Sobolev function classes over the real line R, W<sub>p</sub><sup>r</sup>（R）:={f∈L<sup...Ⅰ. INTRODUCTION AND DEFINITIONLet r be a positive integer and p∈[1, +∞]. We consider the following Sobolev function classes over the real line R, W<sub>p</sub><sup>r</sup>（R）:={f∈L<sup>p</sup>（R）: f<sup>r-1</sup> is locally absolutely continuous on展开更多
基金The project is supported partly by the NationalNatural Science Foundation of China(10071007)and partly by the Foundation for University Key Teachers bythe Ministry of Education of China and partly by the Scientific Research Foundation for Returned Ov
文摘This paper concerns the problem of the Kolmogorov n-width, the linear re-width, the Gel'fand n-width and the Bernstein re-width of Sobolev classes of the periodic multivariate functions in the space Lp(Td) and the average Bernstein o-width, average Kolmogorov o-widths, the average linear o-widths of Sobolev classes of the multivariate functions in the space LP(R ), where p = (p1,…,pd), 1 < Pj < ∞o, j = 1,2,…,d, or pj = ∞,j = 1,2,…, d. Their weak asymptotic behaviors are established for the corresponding quantities.
基金supported by the National Science Foundation of China(No.11161033)Inner Mongolia Normal University Talent Project Foundation(No.RCPY-2-2012-K-036)
文摘Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.
基金Supported by Institution of Higher Education Scientific Research Project in Ningxia(NGY2017011)Natural Science Foundations of Ningxia(NZ15055)+1 种基金Natural Science Foundations of China(1156105511461053)
基金Supported by National Natural Science Foundation of China （Grant Nos. 10671019 and 10971251）, National Natural Science Special-purpose Foundation of China （Grant No. 10826079） and Chinese Universities Scientific Fund （Grant No. 2009-2-05）
文摘For β 〉 0 and an integer r 〉 2, denote by H∞,β those 2π-periodic, real-valued functions f on R, which are analytic in Sβ = {z ∈ C： [ImzI 〈β} and satisfy the restriction If（r）（z）[ ≤ 1, z ∈ Sβ. The optimal quadrature formulae about information composed of the values of a function and its kth （k ： 1,..., r - 1） derivatives on free knots for the classes H∞,β are obtained, and the error estimates of the optimal quadrature formulae are exactly determined.
文摘Ⅰ. INTRODUCTION AND DEFINITIONLet r be a positive integer and p∈[1, +∞]. We consider the following Sobolev function classes over the real line R, W<sub>p</sub><sup>r</sup>（R）:={f∈L<sup>p</sup>（R）: f<sup>r-1</sup> is locally absolutely continuous on
