A Mourre estimate for a Schroedinger operator on a binary tree

1998/07/09 by C. Allard, Christine Shirley Allard, Allard, C. +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/9807007

Latex2e, 12 pages, 2 eps figures included, Presented at the Louisville AMS meeting, March 20-21, 1998

arxiv created 1998/07/09 · openalex publication_date 1998/07/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a binary tree with vertices V and let H be a Schroedinger operator acting on l²(V). A decomposition of the space l²(V) into invariant subspaces is exhibited yielding a conjugate operator A, for use in the Mourre estimate. We show that for potentials q satisfying a first order difference decay condition, a Mourre estimate for H holds.

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