We consider the BVP $-y" + qy = \lambda y$ with $y(0)=y(1)=0$. The inverse spectral problems asks one to recover $q$ from spectral information. In this paper, we present a very simple method to recover a potential by sampling one eigenfunction. The spectral asymptotics imply that for larger modes, more and more information is lost due to imprecise measurements (i.e. relative errors \textit{increases}) and so it is advantageous to use data from lower modes. Our method also allows us to recover "any" potential from \textit{one} boundary condition.
翻译：我们认为 BVP $-y + qy = lambda y $y(0)=y(1)=0美元。 反光谱问题要求从光谱信息中回收$q美元。 在本文中,我们提出了一个非常简单的方法,通过取样一种元功能来恢复潜力。 光谱无症状意味着对于较大的模式来说,由于测量不精确( 相对错误\ textit{ 递增} ), 越来越多的信息丢失了, 因此使用较低模式的数据是有利的。 我们的方法还允许我们从\ textit{one} 边界状态中回收“ 任何” 。
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