Subordinacy Theory for Extended CMV Matrices

Abstract

We develop subordinacy theory for extended CMV matrices. That is, we provide explicit supports for the singular and absolutely continuous parts of the canonical spectral measure associated with a given extended CMV matrix in terms of the presence or absence of subordinate solutions of the generalized eigenvalue equation. Some corollaries and applications of this result are described as well.

25 pages. To appear in Science China Mathematics

References in corpus (3)

• Uniform spectral properties of one-dimensional quasicrystals, III. $\alpha$-continuity
• Almost reducibility and absolute continuity I
• The Hölder continuity of spectral measures of an extended CMV matrix