How to Concentrate Idempotents
نویسنده
چکیده
Call a sum of exponentials of the form f(x) = exp (2πiN1x) + exp (2πiN2x) + · · ·+ exp (2πiNmx), where the Nk are distinct integers, an idempotent. We have L interval concentration if there is a positive constant a, depending only on p, such that for each interval I ⊂ [0, 1] there is an idempotent f so that R I |f (x)| dx R 1 0 |f (x)| dx > a. We will explain how to produce such concentration for each p > 0. The origin of this question and the history of the development of its solution will be surveyed.
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