B-spline quasi-interpolant representations and sampling recovery of functions with mixed smoothness

Dinh Dũng

Let $\xi =\{x^j{\}}_{j=1}^n$ be a grid of $n$ points in the $d$-cube ${\II}^d:=[0,1]^d$, and $\Phi =\{{\varphi }_j{\}}_{j=1}^n$ a family of $n$ functions on ${\II}^d$. We define the linear sampling…