Optimality conjecture for the continuous Kaiser–Bessel shape parameter

Let $m\in\mathbb N\setminus\{1\}$, let $0<\delta\leq \frac{m-1}{m}\pi$, and set

$$\beta=m(\pi-\delta).$$

Consider the Shannon sampling formula with the continuous Kaiser–Bessel window function and uniform approximation error.

Optimality conjecture. The parameter $\beta=m(\pi-\delta)$ is optimal for the Shannon sampling formula with the continuous Kaiser–Bessel window function, as it guarantees the maximum decay rate of the uniform approximation error.

The paper states that this optimality is still an open problem and has so far only been observed numerically.