Dominated splittings and the spectrum of singular quasi-periodic Jacobi operators

Dominated splittings and the spectrum of singular quasi-periodic Jacobi operators

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 R. A. Johnson for Schr\"odinger operators.

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Veröffentlicht in:arXiv.org 2020-08
1. Verfasser: Marx, C A
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Mathematical Physics
Operators
Physics - Mathematical Physics
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Beschreibung
Zusammenfassung: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 R. A. Johnson for Schr\"odinger operators.
ISSN:2331-8422
DOI:10.48550/arxiv.1404.6307