Agmon estimates for the difference of exact and approximate Dirichlet eigenfunctions for difference operators

Abstract

We analyze a general class of difference operators $H_{\epsilon }=T_{\epsilon }+V_{\epsilon }$ on ${\ell }^2(\epsilon {\mathbb{Z}}^d)$, where $V_{\epsilon }$ is a multi-well potential and $\epsilon$ is a small parameter. We construct approximate eigenfunctions in neighbourhoods of the different wells and give weighted ${\ell }^2$-estimates for the difference of these and the exact eigenfunctions of the associated Dirichlet-operators.

20 pages, 1 figure

References in corpus (3)

• Harmonic Approximation of Difference Operators
• Agmon-Type Estimates for a Class of Difference Operators
• Asymptotic Eigenfunctions for a class of Difference Operators

Cited by in corpus (1)

• Tunneling for a class of Difference Operators: Complete Asymptotics