RESOLVENT EXPANSIONS AND CONTINUITY OF THE SCATTERING MATRIX AT EMBEDDED THRESHOLDS: THE CASE OF QUANTUM WAVEGUIDES

摘要

We present an inversion formula which can be used to obtain resolvent expansions near embedded thresholds. As an application, we prove for a class of quantum waveguides the absence of accumulation of eigenvalues and the continuity of the scattering matrix at all thresholds.