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Proceedings of the American Mathematical Society

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Existence of sets of uniqueness of $ l\sp{p}$ for general orthonormal systems


Author: Leonardo Colzani
Journal: Proc. Amer. Math. Soc. 83 (1981), 569-572
MSC: Primary 42C15; Secondary 42C25
DOI: https://doi.org/10.1090/S0002-9939-1981-0627694-8
MathSciNet review: 627694
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Abstract: It is proved that for every orthonormal complete system in $ {L^2}(0,1)$ there exists a set $ A$, of measure arbitrarily close to 1, which carries no nonzero function with Fourier transform in $ {l^p}$, for every $ p < 2$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0627694-8
Article copyright: © Copyright 1981 American Mathematical Society