5 papers · 1 filter
Some constructions of restricted Kakeya sets
Cheng Chen, Jianbin Li, Longhui Li +4
In this paper, we consider Kakeya sets with the additional restriction that centers of the unit line segments belong to a given set. In particular, for every uncountable Borel set…
On unions of geodesics and projections of invariant sets
Longhui Li
Let be a -dimensional complete Riemannian manifold and let denote the canonical projection from the unit tangent bundle. We prove that if is a s…
Fourier Frames on Salem Measures
Longhui Li, Bochen Liu
For every we construct -dimensional Salem measures in the unit interval that do not admit any Fourier frame. Our examples are generic for each , including all exi…
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.…
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 estimates of orthogonal projections. Examples are also discussed. Moreo…