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

Author(s)
Hur, Injo
Issued Date
2018-01
DOI
10.1016/j.jde.2017.09.009
URI
https://scholarworks.unist.ac.kr/handle/201301/22927
Fulltext
http://www.sciencedirect.com/science/article/pii/S0022039617304886?via%3Dihub
Citation
JOURNAL OF DIFFERENTIAL EQUATIONS, v.264, no.1, pp.297 - 310
Abstract
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.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
ISSN
0022-0396
Keyword (Author)
Discrete Schrodinger operatorJacobi operatorCanonical systemWeyl-Titchmarsh m-functionInverse spectral theory
Keyword
INVERSE SPECTRAL THEORYCANONICAL SYSTEMS

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