Cantor spectrum for CMV and Jacobi matrices with coefficients arising from generalized skew-shifts

被引：1

作者：

Jun, Hyunkyu ^{[1
]}

机构：

[1] Rice Univ, Dept Math, Houston, TX 77005 USA

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2022年 / 42卷 / 06期

关键词：

CMV matrices; Jacobi matrices; spectra; cocycle; uniform hyperbolicity; SCHRODINGER-OPERATORS;

D O I：

10.1017/etds.2021.30

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider continuous cocycles arising from CMV and Jacobi matrices. Assuming that the Verblunsky and Jacobi coefficients arise from generalized skew-shifts, we prove that uniform hyperbolicity of the associated cocycles is C-0-dense. This implies that the associated CMV and Jacobi matrices have a Cantor spectrum for a generic continuous sampling map.

引用

页码：2009 / 2027

页数：19

共 37 条

[21] ON SOME MARKOV MATRICES ARISING FROM THE GENERALIZED COLLATZ MAPPING
BUTTSWORTH, RN
MATTHEWS, KR
ACTA ARITHMETICA, 1990, 55 (01) : 43 - 57
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Czechoslovak Mathematical Journal, 2020, 70 : 411 - 433
[25] COMPUTATIONAL METHODS FOR GENERALIZED INVERSE MATRICES ARISING FROM PROPER SPLITTINGS
LAWSON, LM
LINEAR ALGEBRA AND ITS APPLICATIONS, 1975, 12 (02) : 111 - 126
[26] A reciprocal preconditioner for structured matrices arising from elliptic problems with jumping coefficients
Dolgov, Sergey
Khoromskij, Boris N.
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[27] Power series with positive coefficients arising from the characteristic polynomials of positive matrices
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MATHEMATISCHE ANNALEN, 2016, 364 (1-2) : 687 - 707
[28] Power series with positive coefficients arising from the characteristic polynomials of positive matrices
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Mathematische Annalen, 2016, 364 : 687 - 707
[29] On mathematical structures on pairwise comparisons matrices with coefficients in an abstract group arising from quantum gravity
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HELIYON, 2019, 5 (06)
[30] The new inverse eigenvalue problems for periodic and generalized periodic Jacobi matrices from their extremal spectral data
Arela-Perez, S.
Lozano, Charlie
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Pickmann-Soto, H.
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LINEAR ALGEBRA AND ITS APPLICATIONS, 2023, 659 : 55 - 72

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