Schr¨odinger Operators Generated by Substitutions *

Spectral Properties of One-dimensional Schr Odinger Operators with Potentials Generated by Substitutions

We investigate one-dimensional discrete Schrr odinger operators whose potentials are invariant under a substitution rule. The spectral properties of these operators can be obtained from the analysis of a dynamical system, called the trace map. We give a careful derivation of these maps in the general case and exhibit some speciic properties. Under an additional, easily veriiable hypothesis conc...

A Generalization of Gordon ' S Theorem Andapplications to Quasiperiodic Schr

We prove a criterion for absence of eigenvalues for one-dimensional Schrr odinger operators. This criterion can be regarded as an L 1-version of Gor-don's theorem and it has a broader range of application. Absence of eigenvalues is then established for quasiperiodic potentials generated by Liouville frequencies and various types of functions such as step functions, HH older continuous functions...

Exact Smoothing Properties of Schr odinger Semigroups

We study Schr odinger semigroups in the scale of Sobolev spaces and show that for Kato class potentials the range of such semigroups in Lp has exactly two more derivatives than the potential this proves a conjecture of B Simon We show that eigenfunctions of Schr odinger operators are generically smoother by exactly two derviatives in given Sobolev spaces than their potentials We give applicatio...

Locating the Spectrum for Magnetic Schr Odinger and Dirac Operators

Schr Odinger Operators and Fourier Analysis