Riesz sequences and arithmetic progressions

• Autorzy: Itay Londner , Alexander Olevskiĭ
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 42C15: General harmonic expansions, frames

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 225
• Numer: 2
• Strony: 183-191

Daty

wydano

2014

Twórcy

autor

Itay Londner

• School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel

autor

Alexander Olevskiĭ

• School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel

Identyfikatory

DOI

10.4064/sm225-2-5