The Olevskii-Ulanovskii problem on universal Fourier uniqueness

Abstract: The classical Fourier uniqueness theorem states that a function in L²(0,1) is determined by its Fourier coefficients. Equivalently, the exponential system { exp(2πiλx) : λ ∈ ℤ } with integers λ ∈ ℤ is complete in the space L²(S) with S = [0,1]. The Olevskii–Ulanovskii problem asks whether there exists a single irregular point set Λ so that the corresponding exponential system { exp(2πiλx) : λ ∈ Λ } is complete in L²(S) for every set S with sufficiently small measure. In this talk, I will present a recent affirmative answer to this problem and discuss its various extensions and applications. The talk is based on joint work with Susanna Bertolini, Enric Florit-Simon and Mitchell Taylor.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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