Asymptotic Eigenfunctions for a class of Difference Operators

الأصل · EN

We analyze a general class of difference operators Hε = Tε + Vε on ℓ²(ε Zᵈ), where Vε is a one-well potential and ε is a small parameter. We construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low lying eigenvalues of Hε. These are obtained from eigenfunctions or quasimodes for the operator Hε, acting on L²(Rᵈ), via restriction to the lattice ᵈ.