3 papers
math.SP2026
A Complete Proof of the Simon--Lukic Conjecture for Higher-Order Szegő Theorems
Daxiong Piao
This paper provides a complete proof of Simon-Lukic conjecture for orthogonal polynomials on the unit circle. For a probability measure with Verblun…
math.SP2025
The spectrum of the multi-frequency quasi-periodic CMV matrices contains intervals
Bei Zhang, Daxiong Piao
We investigate the spectral structure of multi-frequency quasi-periodic CMV matrices with Verblunsky coefficients defined by shifts on the -dimensional torus. Under the positive…
math.SP2025
Anderson localization for the multi-frequency quasi-periodic CMV matrices and quantum walks
Bei Zhang, Daxiong Piao
In this paper we prove Anderson localization for multi-frequency quasi-periodic extended CMV matrices with analytic Verblunsky coefficients in the regime of positive Lyapunov expon…