Schr Odinger Operators and Fourier Analysis

Locating the Spectrum for Magnetic Schr Odinger and Dirac Operators

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...

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 Class of Matrix-valued Schr Odinger Operators with Prescribed Finite-band Spectra Fritz Gesztesy and Lev

A duality between Schr odinger

The known correspondence between the Kronig{Penney model and certain Jacobi matrices is extended to a wide class of Schrr odinger operators on graphs. Examples include rectangular lattices with and without a magnetic eld, or comb{ shaped graphs leading to a Maryland{type model.