An inverse problem of spectral analysis for a power of the Laplace operator with a potential on a rectangle. (Q1432514)

The authors consider the inverse problem of spectral analysis for an elliptic operator, which is a sum of power \(\beta>0\) of the two-dimensional Laplace operator and the operator of multiplication by a real-valued Lebesgue measurable bounded in an absolute value potential and defined on the rectangle \({0<x<a, 0<y<b}\), where \(a\), \(b\) are given numbers and \(a^{2}b^{-2}\) is an irrational number. They find conditions on the spectral data, when the theorem about the existence of a potential in the inverse problem of spectral analysis holds.