6 papers
Average Nikolskii factors for random diffusion polynomials on closed Riemannian manifolds
Yun Ling, Heping Wang
For , the Nikolskii factor for a diffusion polynomial of degree at most is defined by $$N_{p,q}(P_{\bf a})=\frac{\|P_{\bf a}\|_{q}}{\|P_{\bf a}\…
Average Nikolskii factors for random trigonometric polynomials
Yun Ling, Jiaxin Geng, Jiansong Li +1
For , the Nikolskii factor for a trigonometric polynomial is defined by $$\mathcal N_{p,q}(T_{\bf a})=\frac{\|T_{\bf a}\|_{q}}{\|T_{\bf a}\|_{p}},\…
Optimal quadrature for weighted function spaces on multivariate domains
Jiansong Li, Heping Wang
Consider the numerical integration for weighted Sobolev classes …
Exact Bernstein-Markov inequalities for generalized weights
Jiansong Li, Jiaxin Geng, Yun Ling +1
In this paper, we obtain some exact Bernstein-Markov inequalities for generalized Hermite and Gegenbauer weight. More precisely, we determine the exact values of the extremal…
Weighted least approximation on compact Riemannian manifolds
Jiansong Li, Yun Ling, Jiaxin Geng +1
Given a sequence of Marcinkiewicz-Zygmund inequalities in on a compact space, Gröchenig in \cite{G} discussed weighted least squares approximation and least squares quadratur…
Optimal quadrature errors and sampling numbers for Sobolev spaces with logarithmic perturbation on spheres
Jiaxin Geng, Yun Ling, Jiansong Li +1
In this paper, we study optimal quadrature errors, approximation numbers, and sampling numbers in for Sobolev spaces with logarithmic pert…