On the reconstruction of the potential in an inverse problem of spectral analysis. (Q1432659)

The authors study the inverse problem of spectral analysis for a pseudodifferential elliptic operator, which is the sum of a power of the two-dimensional Laplace operator and the operator of multiplication by a real-valued essentially bounded Lebesgue measurable potential in the rectangle \({0<x<a,\;0<y<b}\), where \(a\), \(b\) are given numbers and \(a^{2}b^{-2}\) is an irrational number. They give conditions for the existence of a potential in the inverse problem of spectral analysis.