Spectral averaging techniques for Jacobi matrices

Spectral averaging techniques for one-dimensional discrete Schroedinger operators are revisited and extended. In particular, simultaneous averaging over several parameters is discussed. Special focus is put on proving lower bounds on the density of the averaged spectral measures. These Wegner type estimates are used to analyze stability properties for the spectral types of Jacobi matrices under local perturbations

Inverse problems for Jacobi operators II: Mass perturbations of semi-infinite mass-spring systems

We consider an inverse spectral problem for infinite linear mass-spring systems with different configurations obtained by changing the first mass. We give results on the reconstruction of the system from the spectra of two configurations. Necessary and sufficient conditions for two real sequences to be the spectra of two modified systems are provided.Comment: 25 pages, 2 figures. Typos were corrected, two remarks were added, material added to Sec.

Singular continuous spectrum is generic

In a variety of contexts, we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators, those with singular spectrum are a dense $G_\delta$.Comment: 5 page