The rotation number for almost periodic potentials with jump discontinuities and $\delta$-interactions

Abstract

We consider one-dimensional Schrödinger operators with generalized almost periodic potentials with jump discontinuities and $\delta$-interactions. For operators of this kind we introduce a rotation number in the spirit of Johnson and Moser. To do this, we introduce the concept of almost periodicity at a rather general level, and then the almost periodic function with jump discontinuities and $\delta$-interactions as an application.

34 pages, to appear in Annales Henri Poincaré

References in corpus (2)

• Schrödinger Operators with Dynamically Defined Potentials: A Survey
• Bethe-Sommerfeld Conjecture and Absolutely Continuous Spectrum of Multi-Dimensional Quasi-Periodic Schrödinger Operators