July 28, 2008
Jonathan Breuer
Title: Reflectionless spectral measures and their application for the spectral analysis of radial trees
We describe a quantum dynamical interpretation, based on joint work with E. Ryckman and B. Simon, of the notion of reflectionless spectral measure. We also show how this notion can be applied to obtain a proof that generic radial metric trees have purely singular continuous spectrum. This last application is joint work with R. Frank and combines the Naimark-Solomyak decomposition for such trees, Simon's Wonderland Theorem, and a recent theorem by C. Remling, dealing with right limits o Schroedinger operators with absolutely continuous spectrum.