Abstract

We consider a class of discrete Schrödinger operators on an infinite homogeneous rooted tree. Potentials for these operators are given by the coefficients of recurrence relations satisfied on a multidimensional lattice by multiple orthogonal polynomials. For operators on a binary tree with potentials generated by multiple orthogonal polynomials with respect to systems of measures supported on disjoint intervals (Angelesco systems) and for compact perturbations of such operators, we show that the essential spectrum is equal to the union of the intervals supporting the orthogonality measures.

中文翻译：

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一棵树上的离散Schrödinger算子，Angeleco势及其扰动

摘要

我们考虑无限均质根树上的一类离散Schrödinger算子。这些算子的电位由多个正交多项式在多维晶格上满足的递归关系系数给出。对于二叉树上具有由多个正交多项式相对于不相交区间支持的测度系统产生的势的算子（Angelesco系统）以及此类算子的紧摄扰动，我们表明基本谱等于支持区间的并集正交性度量。