ON THE ABSOLUTELY CONTINUOUS SPECTRUM OF STURM-LIOUVILLE OPERATORS WITH APPLICATIONS TO RADIAL QUANTUM TREES

被引：12

作者：

Schmied, Michael ^{[1
]}

Sims, Robert ^{[1
]}

Teschl, Gerald ^{[1
,2
]}

机构：

[1] Fac Math, A-1090 Vienna, Austria

[2] Int Erwin Schrodinger Inst Math Phys, A-1090 Vienna, Austria

来源：

OPERATORS AND MATRICES | 2008年 / 2卷 / 03期

基金：

奥地利科学基金会;

关键词：

Sturm-Liouville operators; absolutely continuous spectrum; subordinacy; quantum graphs;

D O I：

10.7153/oam-02-25

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider standard subordinacy theory for general Sturm-Liouville operators and give criteria when boundedness of solutions implies that no subordinate solutions exist. As applications, we prove a Weidmann-type result for general Sturm-Liouville operators and investigate the absolutely continuous spectrum of radially symmetric quantum trees.

引用

页码：417 / 434

页数：18

共 20 条

[1] Absolutely continuous spectra of quantum tree graphs with weak disorder [J].

Aizenman, M ;

Sims, R ;

Warzel, S .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 264 (02) :371-389

[2] Stability of the absolutely continuous spectrum of random Schrodinger operators on tree graphs [J].

Aizenman, Michael ;

Sims, Robert ;

Warzel, Simone .

PROBABILITY THEORY AND RELATED FIELDS, 2006, 136 (03) :363-394

[3]

CARLSON R, 2000, ELECTRON J DIFFER EQ, P1

[4]

Clark S., 1993, DIFFER INTEGRAL EQU, V6, P573

[5] Subordinacy analysis and absolutely continuous spectra for Sturm-Liouville equations with two singular endpoints [J].

Clemence, DP .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1998, 41 (01) :23-27

[6]

Coddington N., 1955, THEORY ORDINARY DIFF

[7] ON SUBORDINACY AND ANALYSIS OF THE SPECTRUM OF ONE-DIMENSIONAL SCHRODINGER-OPERATORS [J].

GILBERT, DJ ;

PEARSON, DB .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1987, 128 (01) :30-56

[8] Dimensional Hausdorff properties of singular continuous spectra [J].

Jitomirskaya, SY ;

Last, Y .

PHYSICAL REVIEW LETTERS, 1996, 76 (11) :1765-1769

[9]

KRUGER H, ARXIV07090127

[10] Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs [J].

Kuchment, P .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2005, 38 (22) :4887-4900

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