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 a...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.展开更多
Using a modified saddle-point method we obtained asymptotic approximation of the r-Stirling numbers of the first and second kind. Here we used a nontrivial trans formation of the same type as that discussed by N.M. Te...Using a modified saddle-point method we obtained asymptotic approximation of the r-Stirling numbers of the first and second kind. Here we used a nontrivial trans formation of the same type as that discussed by N.M. Temme[13], to put the integral representations in volved into a form on which we can apply the saddle point展开更多
In this study, the estimates of approximation numbers of embedding operators in weighted spaces have been analyzed. These estimates depend on orders of differential operators, dimensions of function spaces and weighte...In this study, the estimates of approximation numbers of embedding operators in weighted spaces have been analyzed. These estimates depend on orders of differential operators, dimensions of function spaces and weighted functions. This fact implies that the associated embedding operators belong to Schatten class of compact operators. By using these estimates, the discreetness of spectrum and completion of root elements relating to principal nonselfedjoint degenerate differential operators is obtained.展开更多
基金the National Natural Science Foundation of China(11671271)the Natural Science Foundation of Beijing Municipality(1172004).
文摘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.
文摘Using a modified saddle-point method we obtained asymptotic approximation of the r-Stirling numbers of the first and second kind. Here we used a nontrivial trans formation of the same type as that discussed by N.M. Temme[13], to put the integral representations in volved into a form on which we can apply the saddle point
文摘In this study, the estimates of approximation numbers of embedding operators in weighted spaces have been analyzed. These estimates depend on orders of differential operators, dimensions of function spaces and weighted functions. This fact implies that the associated embedding operators belong to Schatten class of compact operators. By using these estimates, the discreetness of spectrum and completion of root elements relating to principal nonselfedjoint degenerate differential operators is obtained.
