Exponential Riesz bases in L² on two interval

2022/12/02 by Yurii Belov, Belov, Yurii, Mikhail Mironov +1
Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Stability and Controllability of Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2212.02313

openalex publication_date 2022/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give sufficient conditions for the exponential system to be a Riesz basis in L²(E), where E is a union of two intervals. We show that these conditions are close to be necessary. In addition, we demonstrate ``extra point effect'' for such systems, i.e. it may happen that the Riesz basis in L²(E) differs by one point from the Riesz basis on an interval.

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