2021/09/09 by Pfander, Goetz, Shauna Revay, David F. Walnut +2
Mathematics · #42A10 #42A15 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2109.04441
openalex publication_date 2021/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a partition of [0,1] into intervals I1,…,In we prove the existence of a partition of ℤ into Λ1,…, Λn such that the complex exponential functions with frequencies in Λk form a Riesz basis for L2(Ik), and furthermore, that for any J⊆\1, 2, …, n\, the exponential functions with frequencies in \bigcupj∈ JΛj form a Riesz basis for L2(I) for any interval I with length |I|=∑j∈ J|Ij|. The construction extends to infinite partitions of [0,1], but with size limitations on the subsets J⊆ ℤ; it combines the ergodic properties of subsequences of ℤ known as Beatty-Fraenkel sequences with a theorem of Avdonin on exponential Riesz bases.