Extensions to general polynomial decay rates

Investigate analogues of Problems 9.3–9.5 for one-dimensional crystals with ν=1 when the edge-weight decay is w(k)≈|k|^{−p} with p≥1, including determination of spectral types and transport properties under random, generic, and periodic/almost periodic selections of coefficients.

Background

The examples and questions formulated for 1/k^2 decay are natural to extend to other polynomial decays, which remain summable in one dimension for p>1 and are borderline at p=1.

This asks for systematic understanding across decay exponents of how edge presence/absence and structure affect spectra and dynamics.