5 papers
Two Problems in Bergman Spaces with Non-radial Weights
Xiang Fang, Feng Guo, Shengzhao Hou +1
This paper investigates two problems unified by the study of the uniform boundedness of the dilation operators (UBD) T_r f(z)=f(rz), 0<r<1, acting on weighted Bergman spaces A^p_om…
Monotonicity, global symplectification and the stability of Dry Ten Martini Problem
Xianzhe Li, Disheng Xu, Qi Zhou
For any fixed irrational frequency and trigonometric-polynomial potential, we show that every type I energy with positive Lyapunov exponent that satisfies the gap-labelling conditi…
Log-Hausdorff multifractality of the absolutely continuous spectral measure of the almost Mathieu operator
Jie Cao, Xianzhe Li, Baowei Wang +1
This paper focuses on the fractal characteristics of the absolutely continuous spectral measure of the subcritical almost Mathieu operator (AMO) and Diophantine frequency. In parti…
Subordinacy theory for long-range operators: hyperbolic geodesic flow insights and monotonicity theory
Zhenfu Wang, Disheng Xu, Qi Zhou
We introduce a comprehensive framework for subordinacy theory applicable to long-range operators on , bridging dynamical systems and spectral analysis. For finit…
Hyperbolicity for one-frequency analytic quasi-periodic (Hermitian)-symplectic cocycles
Duxiao Wang, Disheng Xu, Qi Zhou
We demonstrate the existence of an open dense subset within the class of real analytic one-frequency quasi-periodic $\mathrm{\Sp}(4,\mathbb{R})$-cocycles, characterized by either t…