Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
183-191
Opis fizyczny
Daty
wydano
2014
Twórcy
autor
- School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
autor
- School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-2-5