5 problems

Let a superoscillation be a portion of a bandlimited function that oscillates faster than the highest frequency contained in its Fourier spectrum, and let its dynamical range mean…

Let a signal be bandlimited if its Fourier spectrum is supported in a finite frequency band. In particular, consider a signal with bandwidth $1\,\mathrm{Hz}$ and a recording consis…

Let $f:[-1,1]\to\mathbb{C}$ admit an extension that is analytic in an open neighborhood of $[-1,1]$. For $0<\epsilon<1$, let $c_f(\epsilon)$ be the smallest positive real number…

For $A>1$, let $\mathcal{C}^+(A)$ denote the relevant Fourier optimization problem, let $J_A^+(F)$ be its objective functional, and let $\mathcal{F}_n$ be the class of nonzero func…

Sharp-gap sampling conjecture. If