Strictly Ergodic Subshifts and Associated Operators

By David Damanik. 2005

64 citations recorded by the source corpus.

We consider ergodic families of Schr\"odinger operators over base dynamics given by strictly ergodic subshifts on finite alphabets. It is expected that the majority of these operators have purely singular continuous spectrum supported on a Cantor set of zero Lebesgue measure. These properties have indeed been established for large classes of operators of this type over the course of the last twenty years. We review the mechanisms leading to these results and briefly discuss analogues for CMV matrices.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/07e88f72a7b77885e2fed9ca6175cdffad07e2b8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. David Damanik
2. Barry Simon
3. David Damanik
4. Doron S. Lubinsky
5. N. H. Bingham
6. Alexander Pushnitski
7. Vilmos Totik
8. Rowan Killip

In Computational Theory and Mathematics

1. Barry Simon
2. David Damanik
3. Doron S. Lubinsky
4. David Damanik
5. Vilmos Totik

In Mathematical Physics

1. David Damanik
2. Barry Simon
3. Doron S. Lubinsky
4. David Damanik
5. Alexander Pushnitski
6. Vilmos Totik

Citations in the corpus

• EQUILIBRIUM MEASURES AND CAPACITIES IN SPECTRAL THEORY (2007, background): “so dµw is for a.e. ωsupported on a countable set, so of zero capacity, consistent with Theorem 2.5. Example 8.6 (Subshifts). This is a rich class of ergodic Jacobi matrices (with an ≡ 1), reviewed in [28] (see also [99, Sect. 12]). For many of them, it is known that E≡ σ(J) is a set of Lebesgue meas”
• Schrödinger operators with dynamically defined potentials (2014, background): “For a more comprehensive survey of the spectral properties of operators associated with subshifts over a finite alphabet, we refer the reader to [64].”