In this paper,a kind of generalized Sobolev-Wiener classes W_(pq)~y(R,h),h>0,defined on the whole real axis,is introduced,and the average σ-K width problem of these function classes in the metric L_q(R)is studied....In this paper,a kind of generalized Sobolev-Wiener classes W_(pq)~y(R,h),h>0,defined on the whole real axis,is introduced,and the average σ-K width problem of these function classes in the metric L_q(R)is studied.For the case p=+∞,1≤q≤+∞,the case 1≤p <+∞,q=1,we get their exact values and identify their optimal subspaces.展开更多
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
The article concerns the average onesided widths of the Sobolev and Besov classes and the classes of functions with bounded moduli of smoothness. The weak asymptotic results are obtained for the corresponding quantities.
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
Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give ...Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give the asymptotic estimates of the n-K widths d_n(W_M(L_r(f)), L_2[0, 1]) and d_n(W_M(K_r(f)), L_2[0, 1]).展开更多
This paper deals with the parallel information-based complexity of numerical integration on Sobolev class. We obtain tight bounds on the complexity, considered as a function of two variables simultaneously:the number ...This paper deals with the parallel information-based complexity of numerical integration on Sobolev class. We obtain tight bounds on the complexity, considered as a function of two variables simultaneously:the number of processors, the rquired precision. This result seems to be new even in serial case.展开更多
This paper concerns the problem of average σ-width of Sobolev–Wiener classes , and Besov-Wiener classes in the metric L q (R d ) for 1 ≤ q ≤ p ≤ ∞. The weak asymptotic results concerning the average linear wid...This paper concerns the problem of average σ-width of Sobolev–Wiener classes , and Besov-Wiener classes in the metric L q (R d ) for 1 ≤ q ≤ p ≤ ∞. The weak asymptotic results concerning the average linear widths, the average Bernstein widths and the infinite-dimensional Gel’fand widths are obtained, respectively.展开更多
文摘In this paper,a kind of generalized Sobolev-Wiener classes W_(pq)~y(R,h),h>0,defined on the whole real axis,is introduced,and the average σ-K width problem of these function classes in the metric L_q(R)is studied.For the case p=+∞,1≤q≤+∞,the case 1≤p <+∞,q=1,we get their exact values and identify their optimal subspaces.
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 Foundation of Education Department of Yunnan Province (07Z10533)Supported partly by the National Natural Science Foundation of China (10471010)+1 种基金partly by the project "Representation Theory and Related Topics" of the "985 program" of Beijing Normal UniversitySupported by the Science Foundation of Yunnan University (2008YB027)
文摘The article concerns the average onesided widths of the Sobolev and Besov classes and the classes of functions with bounded moduli of smoothness. The weak asymptotic results are obtained 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 the National Natural Science Foundation of China(11161033)Supported by the Inner Mongolia Normal University Talent Project Foundation(RCPY-2-2012-K-036)+1 种基金Supported by the Inner Mongolia Normal University Graduate Research Innovation Foundation(CXJJS14053)Supported by the Inner Mongolia Autonomous Region Graduate Research Innovation Foundation(S20141013525)
文摘Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give the asymptotic estimates of the n-K widths d_n(W_M(L_r(f)), L_2[0, 1]) and d_n(W_M(K_r(f)), L_2[0, 1]).
基金this work was supported by china State Major Key Project for Basic Researchers
文摘This paper deals with the parallel information-based complexity of numerical integration on Sobolev class. We obtain tight bounds on the complexity, considered as a function of two variables simultaneously:the number of processors, the rquired precision. This result seems to be new even in serial case.
文摘This paper concerns the problem of average σ-width of Sobolev–Wiener classes , and Besov-Wiener classes in the metric L q (R d ) for 1 ≤ q ≤ p ≤ ∞. The weak asymptotic results concerning the average linear widths, the average Bernstein widths and the infinite-dimensional Gel’fand widths are obtained, respectively.
