Dominated Splittings and the Spectrum for Almost Periodic Jacobi Operators

Abstract

We prove that the resolvent set of any, possibly singular, quasi- periodic Jacobi operator is characterized as the set of all energies whose associated Jacobi cocycles induce a dominated splitting. This extends a well-known result by Johnson for Schrödinger operators.

Publisher

IOP Publishing with London Mathematical Society

Publication Date

12-1-2014

Publication Title

Nonlinearity

Department

Mathematics

Document Type

Article

DOI

https://dx.doi.org/10.1088/0951-7715/27/12/3059

Keywords

Quasi-periodic operators, Spectral theory, Dynamical systems

Language

English

Format

text

Link to Full Text

Share

COinS