4 problems

Orthogonality conjecture. Solutions $f\in\mathcal{A}$ of the Hardy-type integral equation (5.2) are orthogonal with respect to their own zeros for the Jacobi weight.

Let the discrete Fourier transform have eigenstates $f_n(j)\}$, with associated eigenvalue $i^n$, indexed by $n=0,\ldots,N-1$ on a finite set of $N$ points. Mehta's orthogonality c…

General superiority conjecture. The superior performance of dual Laguerre sets over a single Hermite set reflects a general principle: for the relevant class of analytic functions,…

Let $f\in\mathcal{B}_c$, and let … Here $(\varphi^{(c)}_k)_k$ is the scaled Hermite basis of $L^2(\mathbb{R})$, with $\varphi^{(c)}_k(t)=c^{1/4}\varphi_k(\sqrt{c}t)$. Improved Herm…