5 papers
Characterization of Maximizers for Sums of the First Two Eigenvalues of Sturm-Liouville Operators
Gang Meng, Yuzhou Tian, Bing Xie +1
In this paper we study the maximization of the sum of the first two Dirichlet eigenvalues for Sturm-Liouville operators with potentials in the noncompact space . We prove that…
Gap Labelling for Almost Periodic Sturm-Liouville Operators
Gerald Teschl, Yifei Wang, Bing Xie +1
In this paper, we introduce a rotation number for almost periodic Sturm-Liouville operators in the spirit of Johnson and Moser. We then prove the gap labelling theorem in terms of…
On Generalized Strong and Norm Resolvent Convergence
Gerald Teschl, Yifei Wang, Bing Xie +1
We present a streamlined approach for generalized strong and norm convergence of self-adjoint operators in different Hilbert spaces. In particular, we establish convergence of asso…
On the multiplicity of the eigenvalues of discrete tori
Bing Xie, Yigeng Zhao, Yongqiang Zhao
It is well known that the standard flat torus has arbitrarily large Laplacian-eigenvalue multiplicities. We prove, however, that is the optima…
Quantitative estimates for SPDEs on the full space with transport noise and -initial data
Dejun Luo, Bin Xie, Guohuan Zhao
For the stochastic linear transport equation with -initial data () on the full space , we provide quantitative estimates, in negative Sobolev norms, betwe…