具有算子系数的微分算子新的Ambarzumyan定理

摘要

有限区间上具有Neumann边界条件的Sturm-Liouville问题的谱可以唯一确定势函数，这就是经典的Ambarzumyan定理．本文将经典的Ambarzumyan定理推广到有限区间上具有算子系数的二阶与四阶微分算子中．%Ambarzumyan＇s theorem describes the exceptional case in which the spectrum of a single Sturm-Liouville problem with the Neumann boundary conditions on a finite interval uniquely determines the potential. In this paper, the result of Ambarzumyan is extended to second order and fourth order differential operators with operator coefficient in a finite interval.