Reproducing Kernels of Sobolev Spaces on ${\mathbb{R}}^d$ and Applications to Embedding Constants and Tractability

Erich Novak, Mario Ullrich, Henryk Woźniakowski +1

The standard Sobolev space $W_2^s({\mathbb{R}}^d)$, with arbitrary positive integers $s$ and $d$ for which $s>d/2$, has the reproducing kernel $$ K_{d,s}(x,t)=\int_{\mathbb{R}^d}\fra…