STRONG EQUIVALENCES OF APPROXIMATION NUMBERS AND TRACTABILITY OF WEIGHTED ANISOTROPIC SOBOLEV EMBEDDINGS  

作　　者：Jidong HAO Heping WANG 郝季东;汪和平(School of Mathematical Sciences,Capital Normal University,Beijing 100048,China)

机构地区：[1]School of Mathematical Sciences,Capital Normal University,Beijing 100048,China

出　　处：《Acta Mathematica Scientia》2020年第6期1765-1782,共18页数学物理学报（B辑英文版）

基　　金：the National Natural Science Foundation of China(11671271);the Natural Science Foundation of Beijing Municipality(1172004).

摘　　要：In this article,we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a={a j}j≥1 and b={b j}j≥1 of positive numbers.We obtain strong equivalences of the approximation numbers,and necessary and sufficient conditions on a,b to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.

关 键 词：strong equivalences TRACTABILITY approximation numbers weighted anisotropic spaces analytic Korobov spaces 

分 类 号：O177[理学—数学]