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

Article type: Research Article

Authors: Klein, Markus | Rosenberger, Elke^{; *}

Affiliations: Institut für Mathematik, Universität Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany. E-mails: mklein@math.uni-potsdam.de, erosen@uni-potsdam.de, elke.rosenberger@uni-potsdam.de

Correspondence: [*] Corresponding author: Elke Rosenberger, Institut für Mathematik, Universität Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany. E-mail: elke.rosenberger@uni-potsdam.de.

Abstract: We analyze a general class of difference operators Hε=Tε+Vε on ℓ2((εZ)d), where Vε is a multi-well potential and ε is a small parameter. We construct approximate eigenfunctions in neighbourhoods of the different wells and give weighted ℓ2-estimates for the difference of these and the exact eigenfunctions of the associated Dirichlet-operators.

Keywords: semi-classical difference operator, tunneling, WKB-expansions, Dirichlet eigenfunctions, asymptotic expansion, multi-well potential, Agmon estimates

DOI: 10.3233/ASY-151343

Journal: Asymptotic Analysis, vol. 97, no. 1-2, pp. 61-89, 2016