已知部分势函数的AKNS算子的逆谱问题

Inverse spectral results for AKNS systems with partial information on the potentials

考虑定义在[0,1]区间上AKNS算子的逆谱问题。证明了假设2组势函数在区间[a,1](a∈(0,1/2])上已知且它们的差属于Lp空间,若2个系统的共同特征值的数量足够大则这2组势函数相等,且共同特征值的数量与系数p和a有关。

We consider the AKNS systems on the interval[0,1] and prove that two potentials already known on [a,1](a∈(0,1/2])and their difference in Lp are equal if the number of their common eigenvalues is sufficiently large. The result here is to write down explicitly this number in terms of p(and a)showing the role of p.