Singular spectrum for radial trees

Jonathan Breuer; Rupert L. Frank

doi:10.1142/S0129055X09003773

Singular spectrum for radial trees

Jonathan Breuer^*, Rupert L. Frank

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We prove several results showing that absolutely continuous spectrum for the Laplacian on radial trees is a rare event. In particular, we show that metric trees with unbounded edges have purely singular spectrum and that, generically (in the sense of Baire), radial trees have purely singular continuous spectrum.

Original language	English
Pages (from-to)	929-945
Number of pages	17
Journal	Reviews in Mathematical Physics
Volume	21
Issue number	7
DOIs	https://doi.org/10.1142/S0129055X09003773
State	Published - Aug 2009
Externally published	Yes

Bibliographical note

Funding Information:
We are grateful to Barry Simon for useful discussions. RF appreciates the warm hospitality of Caltech, where part of this work has been done, and acknowledges support through DAAD grant D/06/49117.

Keywords

Quantum graphs
Reflectionless property.
Schr̈odinger operators
Singular spectrum
Trees

Access to Document

10.1142/S0129055X09003773

Cite this

@article{3fbc1a6d624c4ab8b237704ad2dec175,

title = "Singular spectrum for radial trees",

abstract = "We prove several results showing that absolutely continuous spectrum for the Laplacian on radial trees is a rare event. In particular, we show that metric trees with unbounded edges have purely singular spectrum and that, generically (in the sense of Baire), radial trees have purely singular continuous spectrum.",

keywords = "Quantum graphs, Reflectionless property., Sch{\"r}odinger operators, Singular spectrum, Trees",

author = "Jonathan Breuer and Frank, {Rupert L.}",

note = "Funding Information: We are grateful to Barry Simon for useful discussions. RF appreciates the warm hospitality of Caltech, where part of this work has been done, and acknowledges support through DAAD grant D/06/49117.",

year = "2009",

month = aug,

doi = "10.1142/S0129055X09003773",

language = "אנגלית",

volume = "21",

pages = "929--945",

journal = "Reviews in Mathematical Physics",

issn = "0129-055X",

publisher = "World Scientific",

number = "7",

}

TY - JOUR

T1 - Singular spectrum for radial trees

AU - Breuer, Jonathan

AU - Frank, Rupert L.

N1 - Funding Information: We are grateful to Barry Simon for useful discussions. RF appreciates the warm hospitality of Caltech, where part of this work has been done, and acknowledges support through DAAD grant D/06/49117.

PY - 2009/8

Y1 - 2009/8

N2 - We prove several results showing that absolutely continuous spectrum for the Laplacian on radial trees is a rare event. In particular, we show that metric trees with unbounded edges have purely singular spectrum and that, generically (in the sense of Baire), radial trees have purely singular continuous spectrum.

AB - We prove several results showing that absolutely continuous spectrum for the Laplacian on radial trees is a rare event. In particular, we show that metric trees with unbounded edges have purely singular spectrum and that, generically (in the sense of Baire), radial trees have purely singular continuous spectrum.

KW - Quantum graphs

KW - Reflectionless property.

KW - Schr̈odinger operators

KW - Singular spectrum

KW - Trees

UR - http://www.scopus.com/inward/record.url?scp=69249179804&partnerID=8YFLogxK

U2 - 10.1142/S0129055X09003773

DO - 10.1142/S0129055X09003773

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:69249179804

SN - 0129-055X

VL - 21

SP - 929

EP - 945

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

IS - 7

ER -

Singular spectrum for radial trees

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this