有限区间并谱的周期性
Periodicity of the spectrum of a finite union of intervals
摘要：
一个勒贝格测度为1的实数集$Ω$称为谱的，如果存在一个实数集$Λ$，使得指数函数$e_λ(x) = \exp(2πi λx)$在$L^2(Ω)$上形成一个完备的规范正交系。这样的集合$Λ$被称为$Ω$的谱。本文给出了一个简化的证明，证明了有限区间并集合$Ω$的谱$Λ$必定是周期的.最初的证明是由于玻色和马丹。
英文摘要：
A set $Ω$, of Lebesgue measure 1, in the real line is called spectral if there is a set $Λ$ of real numbers such that the exponential functions $e_λ(x) = \exp(2πi λx)$ form a complete orthonormal system on $L^2(Ω)$. Such a set $Λ$ is called a spectrum of $Ω$. In this note we present a simplified proof of the fact that any spectrum $Λ$ of a set $Ω$ which is finite union of intervals must be periodic. The original proof is due to Bose and Madan.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
