On a uniqueness theorem for functions with a sparse spectrum

被引：0

作者：

Aleksandrov A.B.

机构：

来源：

Journal of Mathematical Sciences | 2000年 / 101卷 / 3期

基金：

俄罗斯基础研究基金会;

关键词：

Unit Circle; Positive Measure; Uncertainty Principle; Singular Measure; Normalize Lebesgue Measure;

D O I：

10.1007/BF02673729

中图分类号：

学科分类号：

摘要：

We present an example of a set ∧ ∈ double-struck T sign satisfying the following two conditions: (1) there exists a nonzero positive singular measure on the unit circle double-struck T sign with spectrum in ∧; (2) if the spectrum of f ∈ L1 (double-struck T sign) is contained in ∧ and f vanishes on a set of positive measure, then f = 0. ©2000 Kluwer Academic/Plenum Publishers.

引用

页码：3049 / 3052

页数：3