Superoscillations and weak measurement

Band limited functions can oscillate arbitrarily faster than their fastest Fourier component over arbitrarily long intervals Where such b superoscillationsb occur functions are exponentially weak In typical monochromatic optical fields substantial fractions of the domain one third in two dimensions are superoscillatory Superoscillations have implications for signal processing and raise the possibility of sub wavelength resolution microscopy without evanescent waves In quantum mechanics superoscillations correspond to weak measurements in Aharonovb s scheme suggesting b weak valuesb of observables