4 problems

Full-parameter properties conjecture. The following assertions hold:

Positive-coefficient expansion conjecture. For every $n\geq\ell$, this is a convergent series expansion and $A_k^{(\ell,p)}>0$ for every $k\in\mathbb{N}$.

Let $ell\geq3$, let $u\in\ell^{2}(\mathbb{N}_{0})$ satisfy $u_{0}=\dots=u_{\ell-1}=0$, and let … Here $(\nabla u)_{n}=u_{n}-u_{n-1}$, $(\operatorname{div}u)_{n}=u_{n+1}-u_{n}$, and…

Fischer–Keller–Pogorzelski positivity conjecture. All coefficients $c_l$ in this expansion are strictly positive for every $p>1$. The conjecture asserts positivity beyond the integ…