Spectral analysis of the Sturm-Liouville operator on the star-shaped graph

摘要

The Sturm-Liouville operator on the star-shaped graph is considered. We study its spectral properties, important for inverse problem theory. In particular, asymptotic formulas for the weight matrices are derived, by using contour integration. We also prove the Riesz-basis property for a special sequence of vector functions, constructed by the spectral data.