On the determinacy problem for measures

• 成果类型: Article
• 署名作者: Mitkovski, Mishko; Poltoratski, Alexei
• 署名单位: Clemson University; Texas A&M University System; Texas A&M University College Station
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0588-6
• 发表日期: 2015
• 页码: 1241-1267
• 关键词: spectral gap; oscillation

摘要

We study the general moment problem for measures on the real line, with polynomials replaced by more general spaces of entire functions. As a particular case, we describe measures that are uniquely determined by a restriction of their Fourier transform to a finite interval. We apply our results to prove an extension of a theorem by Eremenko and Novikov on the frequency of oscillations of measures with a spectral gap (high-pass signals) near infinity.