This article is a improvement on author＇s early work （Acta Mathematica Scientia, Vol.30 No.2 Ser.A 2010）. In this article, there are two new contributions： 1） The restrictive conditions on approximation domain bo...This article is a improvement on author＇s early work （Acta Mathematica Scientia, Vol.30 No.2 Ser.A 2010）. In this article, there are two new contributions： 1） The restrictive conditions on approximation domain boundary is improved essentially. 2） The Fejer points is extended by perturbed Fejer points with stable order of approximation.展开更多
This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterization...This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besom spaces B(?)(0,1) with 0<σ<∞ and (1+σ)-1<γ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.展开更多
基金supported by NSF of Henan Province P. R. China(974050900)
文摘This article is a improvement on author＇s early work （Acta Mathematica Scientia, Vol.30 No.2 Ser.A 2010）. In this article, there are two new contributions： 1） The restrictive conditions on approximation domain boundary is improved essentially. 2） The Fejer points is extended by perturbed Fejer points with stable order of approximation.
基金The work of the author has been supported by the Deutache Forschungsgemeinschaft(DFG) under Grant Ho 1846/1-1
文摘This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besom spaces B(?)(0,1) with 0<σ<∞ and (1+σ)-1<γ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
