5 problems

Lorentz-space approximation and Gelfand number conjecture. Formula…

For $1\leq p\leq2\leq q\leq\infty$, define … Let $a_n$ denote the $n$th approximation number of the embedding. The piecewise approximation-number conjecture. There is a universal c…

The Gelfand–approximation conjecture. One has

GKS's conjecture. The approximation numbers satisfy

Let $D_d$ be a bounded nonempty open subset of $\mathbb{R}^d$, and let $H^r(D_d)$ be a Sobolev space for which the approximation problem is defined. Let $H^r_0(D_d)$ be the closure…