Longhui Li

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20242026

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4 papers · 1 filter

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.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.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…