  A function f is said to possess superoscillations if, in a finite region, f
oscillates faster than the shortest wavelength that occurs in the Fourier
transform of f. I will discuss four aspects of superoscillations: 1.
Superoscillations can be generated efficiently and stably through
multiplication. 2. There is a win-win situation in the sense that even in
circumstances where superoscillations cannot be used for superresolution, they
can be useful for what may be called superabsorption, an effective
up-conversion of low frequencies 3. The study of superoscillations may be
useful for generalizing the Shannon Hartley noisy channel capacity theorem. 4.
The phenomenon of superoscillations naturally generalizes beyond bandlimited
functions.
