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.
The present paper deals with best onesided approximation rate in L p spaces n(f) L p of f∈C 2π. Although it is clear that the estimate n(f) L p≤C‖f‖ L p cannot be correct for all f∈L ...The present paper deals with best onesided approximation rate in L p spaces n(f) L p of f∈C 2π. Although it is clear that the estimate n(f) L p≤C‖f‖ L p cannot be correct for all f∈L p 2π in case p<∞, the question whether n(f) L p≤Cω(f,n -1) L p or n(f) L p≤CE n(f) L p holds for f∈C 2π remains totally untouched. Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis.展开更多
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 in part by National and Zhejiang Provincial Natural Science Foundations of China.Partof the work contained in this paper was done while the second named author was visiting Simon Fraser University,Canada,he thanks Dr.P.B.Borwein and the Depa
文摘The present paper deals with best onesided approximation rate in L p spaces n(f) L p of f∈C 2π. Although it is clear that the estimate n(f) L p≤C‖f‖ L p cannot be correct for all f∈L p 2π in case p<∞, the question whether n(f) L p≤Cω(f,n -1) L p or n(f) L p≤CE n(f) L p holds for f∈C 2π remains totally untouched. Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis.
