论文标题
具有限制支持的复杂指数基础
Bases of complex exponentials with restricted supports
论文作者
论文摘要
具有整数频率的复杂指数构成了单位间隔上方形积分函数空间的基础。如果复杂指数的支持仅限于单位间隔的子集重叠，我们分析是否维持基础属性。 We show, for example, that if $S_1, \ldots, S_K \subset [0,1]$ are finite unions of intervals with rational endpoints that cover the unit interval, then there exists a partition of $\mathbb{Z}$ into sets $Λ_1, \ldots, Λ_K$ such that $\bigcup_{k=1}^K \{ e^{2πiλ（\ cdot）}χ_{s_k}：λ_k\} $是$ l^2 [0,1] $的riesz基础。在这里，$χ_s$表示$ S $的特征功能。
The complex exponentials with integer frequencies form a basis for the space of square integrable functions on the unit interval. We analyze whether the basis property is maintained if the support of the complex exponentials is restricted to possibly overlapping subsets of the unit interval. We show, for example, that if $S_1, \ldots, S_K \subset [0,1]$ are finite unions of intervals with rational endpoints that cover the unit interval, then there exists a partition of $\mathbb{Z}$ into sets $Λ_1, \ldots, Λ_K$ such that $\bigcup_{k=1}^K \{ e^{2πi λ(\cdot)} χ_{S_k} : λ\in Λ_k \}$ is a Riesz basis for $L^2[0,1]$. Here, $χ_S$ denotes the characteristic function of $S$.
