5 papers · 1 filter
Growth of Eigenfunctions and R-limits on Graphs
Siegfried Beckus, Latif Eliaz
A characterization of the essential spectrum of Schrödinger operators on infinite graphs is derived involving the concept of -limits. This concept, whi…
Generalized eigenfunctions and eigenvalues: a unifying framework for Shnol-type theorems
Siegfried Beckus, Baptiste Devyver
Let be a generalized Schrödinger operator on a domain of a non-compact connected Riemannian manifold, and a generalized eigenfunction for : that is, satisfies the eq…
Hölder Continuity of the Spectra for Aperiodic Hamiltonians
Siegfried Beckus, Jean Bellissard, Horia Cornean
We study the spectral location of strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to…
Spectral Continuity for Aperiodic Quantum Systems II. Periodic Approximations in 1D
Siegfried Beckus, Jean Bellissard, Giuseppe De Nittis
The existence and construction of periodic approximations with convergent spectra is crucial in solid state physics for the spectral study of corresponding Schrödinger operators. I…
Shnol-type theorem for the Agmon ground state
Siegfried Beckus, Yehuda Pinchover
Let be a Schrödinger operator defined on a noncompact Riemannian manifold , and let . Suppose that the operator is critical in , and le…