6 problems

Uniform lower-bound conjecture. There exists a constant $C>0$, independent of $d$ and $D_d$, such that

Novak's conjecture. The matrix

Let $\widetilde{F}_d$ be the class of smooth functions on $[0,1]^d$ defined by … Consider the question whether integration on this class suffers from the curse of dimensionality, a…

Let $(a_j)_{j\geq 1}$ and $(b_j)_{j\geq 1}$ be the sequences defining the Hermite space, and let EC-WT denote exponential-convergence weak tractability. Sufficient-condition conjec…

Let $B_{\mathbb R^d}$ denote the unit ball in $\mathbb R^d$, and consider ridge functions of the form … where $a\in\mathbb R^d$ satisfies $\|a\|_{\ell_2^d}=1$ and, for some…

Let $F_d=C^{r(d)}([0,1]^d)$ be the space of functions on the $d$-dimensional unit cube with $r(d)$ continuous derivatives, equipped with the supremum norm of all partial derivative…