Existence of sets of uniqueness of 𝑙^{𝑝} for general orthonormal systems

Colzani, Leonardo

doi:10.1090/S0002-9939-1981-0627694-8

Existence of sets of uniqueness of $l^{p}$ for general orthonormal systems
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Proc. Amer. Math. Soc. 83 (1981), 569-572 Request permission

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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