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math.SP2026
Dry Ten Martini Problem in the Subcritical Type I Regime
Xianzhe Li
We establish a resolvent factorization of the hyperbolic projection associated with the finite-range dual operators, by a kernel with exponential off-diagonal decay. As an applicat…
math.SP2026
Transfer Operators, Canonical Center Dynamics, and Spectral Applications for Long-Range Operators
Xianzhe Li, Zhenfu Wang, Jiangong You +1
We introduce an operator-theoretic framework for long-range operators over general dynamical systems with analytic hopping and small potential. By establishing a partially hyperbol…
math.SP2022★ 1 cited
Stability of Spectral Types of Quasi-Periodic Schrödinger Operators With Respect to Perturbations by Decaying Potentials
David Damanik, Xianzhe Li, Jiangong You +1
We consider perturbations of quasi-periodic Schrödinger operators on the integer lattice with analytic sampling functions by decaying potentials and seek decay conditions under whi…