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Distributed Spectral Pairs for the Fractal Uncertainty Principle on Cantor Sets

A necessary and sufficient condition for a discrete self-similar Cantor set to attain the largest possible ('most uncertain') exponent (1-delta)/2 in the fractal uncertainty principle. The condition is expressed through 'distributed spectral pairs', a generalization of Fuglede's spectral pairs, and includes a classification of which subsets of certain cyclic groups form such pairs, with an extension of the analysis to the continuous setting.