5 papers
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}},\…
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…
On the power of standard information for tractability for approximation of periodic functions in the worst case setting
Jiaxin Geng, Heping Wang
We study multivariate approximation of periodic function in the worst case setting with the error measured in the norm. We consider algorithms that use standard informat…