Uniform spectral properties of one-dimensional quasicrystals. III: \(\alpha\)-continuity. (English) Zbl 1045.81024
Summary: We study the spectral properties of one-dimensional whole-line Schrödinger operators, especially those with Sturmian potentials. Building upon the Jitomirskaya-Last extension of the Gilbert-Pearson theory of subordinacy, we demonstrate how to establish \(\alpha\)-continuity of a whole-line operator from power-law bounds on the solutions on a half-line. However, we require that these bounds hold uniformly in the boundary condition.
Parts I, II, cf. Commun. Math. Phys. 207, No. 3, 687-696 (1999; Zbl 0962.81012) and Lett. Math. Phys. 50, No. 4, 245-257 (1999; Zbl 1044.81036).
Parts I, II, cf. Commun. Math. Phys. 207, No. 3, 687-696 (1999; Zbl 0962.81012) and Lett. Math. Phys. 50, No. 4, 245-257 (1999; Zbl 1044.81036).
MSC:
81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
39A70 | Difference operators |
47B36 | Jacobi (tridiagonal) operators (matrices) and generalizations |
47B39 | Linear difference operators |
47N55 | Applications of operator theory in statistical physics (MSC2000) |