Inverse spectral problems for functional-differential operators with involution

The main goal of this paper is to propose an approach inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the second-order FDO involution-reflection. Our based reduction problem matrix form and solution Sturm-Liouville operator by developing method mappings. obtained contains weight, which causes qualitative difficulties in study problem. As a result, show that considered involution uniquely specified five spectra certain regular boundary value problems.