Longhui Li

activity

20242026

collaborators

6 papers

math.CA2026

Dimension of Diophantine approximation and some applications in harmonic analysis

Longhui Li, Bochen Liu

In this paper we construct a new family of sets based on Diophantine approximation in the Euclidean space, and consider their applications in several problems in harmonic analysis.…

math.CA2026

On unions of geodesics and projections of invariant sets

Longhui Li

Let $M$ be a $d$ -dimensional complete Riemannian manifold and let $I ¨ : S M \to M$ denote the canonical projection from the unit tangent bundle. We prove that if $E \subset S M$ is a…

math.SP2025

On the Kotani-Last Conjecture for the Dirac Operator

Nyah Davis, Ãris EmilsdÃ³ttir, Long Li +1

We prove a dichotomy of almost periodicity for reflectionless one-dimensional Dirac operators whose spectra satisfy certain geometric conditions, extending work of Volberg--Yuditsk…

math.CA2025

Fourier Frames on Salem Measures

Longhui Li, Bochen Liu

For every $0 < s \leq 1$ we construct $s$ -dimensional Salem measures in the unit interval that do not admit any Fourier frame. Our examples are generic for each $s$ , including all exi…

math-ph2025

Twenty dry Martinis for the Unitary Almost Mathieu Operator

Christopher Cedzich, Long Li

We solve the Dry Ten Martini Problem for the unitary almost Mathieu operator with Diophantine frequencies in the non-critical regime.

math.CA2024

Orthogonal projection, dual Furstenberg problem, and discretized sum-product

Longhui Li, Bochen Liu

In this paper we come up with a dual version of the Furstenberg problem and obtain partial results via $L^{p}$ estimates of orthogonal projections. Examples are also discussed. Moreo…