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Riesz sequences and arithmetic progressions

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Londner I., Olevskiĭ A.

Studia Mathematica

2014

tom 225

nr 2

183-191

Given a set 𝓢 of positive measure on the circle and a set Λ of integers, one can ask whether $E(Λ) := e^{iλt}_{λ∈Λ}$ is a Riesz sequence in L²(𝓢). We consider this question in connection with some arithmetic properties of the set Λ. Improving a result of Bownik and Speegle (2006), we construct a set 𝓢 such that E(Λ) is never a Riesz sequence if Λ contains an arithmetic progression of length N and step $ℓ = O(N^{1-ε})$ with N arbitrarily large. On the other hand, we prove that every set 𝓢 admits a Riesz sequence E(Λ) such that Λ does contain arithmetic progressions of length N and step ℓ = O(N) with N arbitrarily large.

Ograniczanie wyników

1 Studia Mathematica

1 Londner I.

1 Olevskiĭ A.

1 2014

Wyniki wyszukiwania

Riesz sequences and arithmetic progressions