Multilevel interpolation for Nikishin systems and boundedness of Jacobi matrices on binary trees

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.1070/RM10017

A. Aptekarev, V. Lysov

引用次数: 2

Abstract

Modern applications [1] provide motivation to consider the tridiagonal Jacobi matrix (or the so-called discrete Schrödinger operator), a classical object of spectral theory, on graphs [2]. On homogeneous trees one method to implement such operators is based on Hermite–Padé interpolation problems (see [3]). Let μ⃗ = (μ1, . . . , μd) be a collection of positive Borel measures with compact supports on R. We denote by μ̂j(z) := ∫ (z−x)−1 dμj(x) their Cauchy transforms. For an arbitrary multi-index n⃗ ∈ Z+, we need to find polynomials qn⃗,0, qn⃗,1, . . . , qn⃗,d and pn⃗, pn⃗,1, . . . , pn⃗,d with deg pn⃗ = |n⃗| := n1 + · · · + nd such that the following interpolation conditions are satisfied as z →∞ for j = 1, . . . , d:

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Nikishin系统的多级插值及二叉树上Jacobi矩阵的有界性

现代应用[1]提供了在图[2]上考虑三对角Jacobi矩阵(或所谓的离散Schrödinger算子)的动机，这是谱理论的一个经典对象。在齐次树上实现这种算子的一种方法是基于hermite - pad插值问题(见[3])。令μ∈(μ1，…)， μd)是r上具有紧支撑的正Borel测度的集合，用μ μj(z) =∫(z−x)−1 dμj(x)表示它们的柯西变换。对于任意多指标n∈Z+，我们需要找到多项式qn l2,0, qn l2,1，…。， qn,d和pn, pn,1，…， pn∈，d与deg pn∈= |n∈|:= n1 +···+，且对于j = 1，…，满足下列插值条件:z→∞d:

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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