In this paper we prove that there exists a constant C such that, if S,S are subsets of of finite measure, then for every function ,where is the Fourier transform of f and w(S) is the mean width of S. This extends to dimension d1 a result of Nazarov [Local estimates for exponential polynomials and their applications to inequalities of the uncertainty principle type, Algebra i Analiz 5 (1993) 3�66 (in Russian); translation in St. Petersburg Math. J. 5 (1994) 663�717] in dimension d=1.
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