The m-functions of discrete Schrodinger operators are sparse compared to those for Jacobi operators

被引：2
|
作者：
Hur, Injo [1 ]
机构：
[1] Ulsan Natl Inst Sci & Technol, Dept Math Sci, Ulsan, South Korea
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 264卷 / 01期
基金：
新加坡国家研究基金会;
关键词：
Discrete Schrodinger operator; Jacobi operator; Canonical system; Weyl-Titchmarsh m-function; Inverse spectral theory; INVERSE SPECTRAL THEORY; CANONICAL SYSTEMS;
D O I：
10.1016/j.jde.2017.09.009
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We explore the sparsity of Weyl-Titchmarsh m-functions of discrete Schrodinger operators. Due to this, the set of their m-functions cannot be dense on the set of those for Jacobi operators. All this reveals why an inverse spectral theory for discrete Schrodinger operators via their spectral measures should be difficult. To obtain the result, de Branges theory of canonical systems is applied to work on them, instead of Weyl-Titchmarsh m-functions. (C) 2017 Elsevier Inc. All rights reserved.
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页码：297 / 310
页数：14
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