Generic spectral results for CMV matrices with dynamically defined Verblunsky coefficients

被引：7

作者：

Fang, Licheng ^{[1
]}

Damanik, David ^{[2
]}

Guo, Shuzheng ^{[1
,2
]}

机构：

[1] Ocean Univ China, Qingdao 266100, Shandong, Peoples R China

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

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2020年 / 279卷 / 12期

关键词：

CMV matrices; Ergodic Verblunsky coefficients; Kotani theory; SCHRODINGER-OPERATORS; TRACE CLASS; POLYNOMIALS;

D O I：

10.1016/j.jfa.2020.108803

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider CMV matrices with dynamically defined Verblunsky coefficients. These coefficients are obtained by continuous sampling along the orbits of an ergodic transformation. We investigate whether certain spectral phenomena are generic in the sense that for a fixed base transformation, the set of continuous sampling functions for which the spectral phenomenon occurs is residual. Among the phenomena we discuss are the absence of absolutely continuous spectrum and the vanishing of the Lebesgue measure of the spectrum. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：22

共 24 条

[1]

[Anonymous], 1990, Probability and its Applications, DOI [10.1007/978-1-4939-0512-6_4, DOI 10.1007/978-1-4939-3271-9_6]

[2] Generic singular spectrum for ergodic Schrodinger operators [J].

Avila, A ;

Damanik, D .

DUKE MATHEMATICAL JOURNAL, 2005, 130 (02) :393-400

[3] A CONDITION FOR UNIQUE ERGODICITY OF MINIMAL SYMBOLIC FLOWS [J].

BOSHERNITZAN, MD .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1992, 12 :425-428

[4] Generic continuous spectrum for ergodic Schrodinger operators [J].

Boshernitzan, Michael ;

Damanik, David .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2008, 283 (03) :647-662

[5] The repetition property for sequences on tori generated by polynomials or skew-shifts [J].

Boshernitzan, Michael ;

Damanik, David .

ISRAEL JOURNAL OF MATHEMATICS, 2009, 174 (01) :189-202

[6] UNITARY EQUIVALENCE MODULO TRACE CLASS FOR SELF-ADJOINT OPERATORS [J].

CAREY, RW ;

PINCUS, JD .

AMERICAN JOURNAL OF MATHEMATICS, 1976, 98 (02) :481-514

[7]

CAREY RW, 1974, P AM MATH SOC, V45, P229

[8]

Cycon HL., 1987, TEXTS MONOGRAPHS PHY, DOI 10.1007/978-3-540-77522-5

[9]

Damanik D., SUBSHIFTS SATI UNPUB

[10]

Damanik D., Spectral Theory of Discrete One -Dimensional Ergodic Schrodinger Operators

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