Multivariate approximation by translates of the Korobov function on Smolyak grids

Dinh Dung, Charles Micchelli

For a set $\mathbb{W} \subset L_p(\bT^d)$, $1<p<\infty$, of multivariate periodic functions on the torus $\bT^d$ and a given function $φ\in L_p(\bT^d)$, we study the approximat…