Aharon Casher discusses the bounds on the norm of Super-oscillatory functions. Super-oscillatory functions are functions whose Fourier transform has a bounded support but exhibit high wave numbers in a limited range of coordinate space. A lower bound on the norm of such functions is derived. The bound tends to infinity with the range.
Casher, Aharon, "Bounds on the Norms of Super-Oscillatory Functions" (2012). Physics Lectures. 2.