8 papers
The Local Embedding Problem for Hardy Spaces of Dirichlet Series
Bonan Chen, Xiang Fang, Feng Guo +3
We solve the local embedding problem for Hardy spaces of Dirichlet series, which is a dimension-free trace problem asking whether the global -norm controls local $L^…
A Functional Central Limit Theorem for Window Counts of Hardy--Szegő Zeros
Qian Ai, Feng Guo, Qi Zhou
The Hardy--Szegő zero process, investigated in the disk by Peres and Virág through the independent identically distributed Gaussian analytic function, is a canonical conformally in…
Two Regularity Problems on Analytic Tent Spaces
Xiang Fang, Feng Guo, Shengzhao Hou +2
We study two regularity problems on Hardy-type analytic tent spaces on the unit disk: fractional integration and randomization of Taylor coefficients. For fr…
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
We prove that, for every irrational frequency and every analytic Type I potential, each supercritical spectral energy satisfying the gap-labelling condition is an endpoint of an op…
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…