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math.SP2026
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…
math.SP2026
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…
math.SP2024
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…