Xiaolong Han

Small scale quantum ergodicity in negatively curved manifolds

In this paper, we investigate quantum ergodicity in negatively curved manifolds. We consider the symbols depending on a semiclassical parameter h with support shrinking down to a point as . The rate of shrinking is a power of . This extends the asymptotic equidistribution of quantum ergodic eigenfunctions to a logarithmical scale.

Small Scale Equidistribution of Random Eigenbases

We investigate small scale equidistribution of random orthonormal bases of eigenfunctions (i.e., eigenbases) on a compact manifold

\(L^p\) Bilinear Quasimode Estimates

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Characterization of balls in terms of Bessel-potential integral equation☆

M. Assume that the group of isometries acts transitively on

Hardy–Littlewood–Sobolev and Stein–Weiss inequalities and integral systems on the Heisenberg group

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Sharp norm estimates of layer potentials and operators at high frequency

M and the multiplicity