collaborators

10 papers

math.DS2026

Positivity and log-Hölder Continuity of Lyapunov Exponents for Multi-Frequency Skew-Shift Schrödinger Operators

Chao Wang, Yuanyuan Peng, Daxiong Piao

We prove the positivity and continuity of the Lyapunov exponent for one-dimensional discrete Schrödinger operators with multi-frequency skew-shift potentials. For the operator $H_…

math.DS2026

Construction and Characterization of Oscillatory Chain Sequences

Zejun Dai, Daxiong Piao, Jinglai Qiao

This paper initiates a theoretical investigation of -oscillatory chain sequences , generalizing Szwarc's classical framework for non-oscillatory chains \cite{…

math.SP2026

Necessary Conditions for Single-Critical-Point Higher-Order Szegő Sum Rules in OPUC

Daxiong Piao

We prove the necessity part of the higher-order Szegő theorem on the unit circle for the single-critical-point weights , . If …

math.SP2026

On the Genericity of the Spectrum Intervalization for Multi-Frequency Quasiperiodic Schrödinger Operators

Daxiong Piao

This paper proves a genericity conjecture by Goldstein, Schlag, and Voda[Invent. Math.\textbf{217}(2019)] for multi-frequency quasiperiodic Schrödinger operators. Specifically, we…

math.CA2026

Single-Point Higher-Order Szegő Sum Rules in OPUC: Necessity for

Daxiong Piao

We give a direct algebraic proof of the necessity direction in the single-point higher-order Szegő sum rules on the unit circle for . More precisely, for $H_m(e^{iθ})=(1…

math.SP2026

Finite and full scale localization for the multi-frequency quasi-periodic CMV matrices

Bei Zhang, Daxiong Piao

This paper formulates the finite and full-scale localization for multi-frequency quasi-periodic CMV matrices. This can be viewed as the CMV counterpart to the localization results…