10 problems

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…

Let $m:[-pi,pi]to ot i e R{geq 0}$ be a non-negative continuous function, and for each integer $N etextgreater=1$ define … Let $\phi_{\mathrm{Newman}}(k,N)$ denote the Newman phase…

De Bièvre's conjecture. The state $|\psi\rangle$ is Kirkwood–Dirac classical if and only if

Let ${\boldsymbol{m}{A}}$ be a DFT matrix and let ${y_i}$ denote the resulting measurement values. DFT measurement dynamic-range conjecture. The dynamic range of the ${y_i}$ values…

Structured discrete Hankel-transform conjecture. The following pairs are feasible:

Discrete square-size conjecture.

Discrete Fourier-transform feasibility conjecture. If $(k,q)$ is $s$-feasible, then $(k+1,q)$ and $(k,q-1)$ are $s$-feasible. The function $q\mapsto\mathbb{A}_s^{\textup{disc}}(q)$…

Let $\{\mathbf{T}_n\}_{0\le n<N}$ be the minimal Hermite-type basis of $\mathbb{R}^N$, and let $\psi_n$ denote the corresponding Hermite functions. Convergence conjecture. The vect…

Let $I_N$ be the index set used for the discrete Fourier transform, and let ${\boldsymbol\phi}_n\in\mathbb R^N$ be the constructed eigenvectors. Define the number of zero crossings…

Let $N=4L+1$, let $I_N$ be the index set used for the discrete Fourier transform, and let ${\boldsymbol\phi}_n$ be the orthonormal eigenvectors constructed in the paper. Set … Let…