Jialun Li

activity

20182022

collaborators

5 papers

math.DS2022

Equidistribution and counting of periodic flat tori

Nguyen-Thi Dang, Jialun Li

Let $G$ be a semisimple Lie group without compact factor and $Γ < G$ a torsion-free, cocompact, irreducible lattice. According to Selberg, periodic orbits of regular Weyl chamber fl…

math.DS2019

Fourier transform of self-affine measures

Jialun Li, Tuomas Sahlsten

Suppose $F$ is a self-affine set on $R^{d}$ , $d \geq 2$ , which is not a singleton, associated to affine contractions $f_{j} = A_{j} + b_{j}$ , $A_{j} \in GL (d, R)$ , $…

math.CA2018

Discretized Sum-product and Fourier decay in $R^{n}$

Jialun Li

We generalize Bourgain's theorem on the decay of the Fourier transform of the multiplicative convolution of measures on $R$ to the ring $R^{n}$ , where the multiplicat…

math.DS2018

Fourier decay, Renewal theorem and Spectral gaps for random walks on split semisimple Lie groups

Jialun Li

We establish an exponential error term for the renewal theorem in the context of products of random matrices, which is surprising compared with classical abelian cases. A key tool…

math.SP2018

Finiteness of Small Eigenvalues of Geometrically Finite Rank one Locally Symmetric Manifolds

Jialun Li

Let M be a geometrically finite rank one locally symmetric manifolds. We prove that the spectrum of the Laplace operator on M is finite in a small interval which is optimal.

Equidistribution and counting of periodic flat tori

Fourier transform of self-affine measures

Discretized Sum-product and Fourier decay in Rn

Fourier decay, Renewal theorem and Spectral gaps for random walks on split semisimple Lie groups

Finiteness of Small Eigenvalues of Geometrically Finite Rank one Locally Symmetric Manifolds

Discretized Sum-product and Fourier decay in $R^{n}$