Abstract
A canonical superoscillatory function, defined on the circle, satisfies a set of uncertainty inequalities for periodic functions, strengthened by an anticommutator term introduced by Schrödinger. The superoscillations can be made to dominate the uncertainty inequality by selecting them with a sufficiently narrow window. The uncertainty product, and its minimum value, are calculated as functions of the window width, as well as their asymptotics for narrow and wide windows. The function has minimum uncertainty only for very narrow windows.
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