36 citations · 389 across the 48 of their papers we have counts for
6 papers · 1 filter
Continuous quasiperiodic Schrödinger operators with Gordon type potentials
Wencai Liu
Let us concern the quasi-periodic Schrödinger operator in the continuous case, \begin{equation*} (Hy)(x)=-y^{\prime\prime}(x)+V(x,ωx)y(x), \end{equation*} where …
Sharp bound on the largest positive eigenvalue for one-dimensional Schrödinger operators
Wencai Liu
Let be a Schrödinger operator on , or on . Suppose the potential satisfies . We prove that a…
Some refined results on mixed Littlewood conjecture for pseudo-absolute values
Wencai Liu
In this paper, we study the mixed Littlewood conjecture with pseudo-absolute values. For any pseudo absolute value sequence , we obtain the sharp criterion such that f…
Growth of the eigensolutions of Laplacians on Riemannian manifolds II: positivity of the initial energy
Wencai Liu
In this paper, energy function is used to investigate the eigen-solutions of on the Riemannian manifolds. We give a new way to prove the positivity of the initial ener…
Growth of the eigensolutions of Laplacians on Riemannian manifolds I: construction of energy function
Wencai Liu
In this paper, we consider the eigen-solutions of , where is the Laplacian on a non-compact complete Riemannian manifold. We develop Kato's methods on manifold and…
Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies
Wencai Liu, Yunfeng Shi
We prove that the size of the spectral gaps of weakly coupled quasi-periodic Schrödinger operators with Liouville frequencies decays exponentially. As an application, we obtain the…