6 papers
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…
On the Kotani-Last Conjecture for the Dirac Operator
Nyah Davis, íris Emilsdóttir, 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…
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…
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.
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.…