Spectral Multiplicity of Selfadjoint Schrödinger Operators on Star-Graphs with Standard Interface Conditions

Standard

Spectral Multiplicity of Selfadjoint Schrödinger Operators on Star-Graphs with Standard Interface Conditions. / Simonov, Sergey; Woracek, Harald.

In: Integral Equations and Operator Theory, Vol. 78, No. 4, 2014, p. 523-575.

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

BibTeX

@article{e13552f4f7344c42a1f47b8658e5f45e,

title = "Spectral Multiplicity of Selfadjoint Schr{\"o}dinger Operators on Star-Graphs with Standard Interface Conditions",

abstract = "We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schr{\"o}dinger operator on a star-shaped graph with continuity and Kirchhoff conditions at the interior vertex. We compute the multiplicity of the singular spectrum in terms of the spectral measures of the Weyl functions associated with the single (independently considered) boundary relations. This result is a generalization and refinement of a Theorem of I.S.Kac.",

keywords = "boundary relations, Herglotz functions, quantum graphs, Schr{\"o}dinger operators, singular spectrum, spectral multiplicity, Weyl theory",

author = "Sergey Simonov and Harald Woracek",

year = "2014",

doi = "10.1007/s00020-013-2106-9",

language = "English",

volume = "78",

pages = "523--575",

journal = "Integral Equations and Operator Theory",

issn = "0378-620X",

publisher = "Birkh{\"a}user Verlag AG",

number = "4",

}

RIS

TY - JOUR

T1 - Spectral Multiplicity of Selfadjoint Schrödinger Operators on Star-Graphs with Standard Interface Conditions

AU - Simonov, Sergey

AU - Woracek, Harald

PY - 2014

Y1 - 2014

N2 - We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schrödinger operator on a star-shaped graph with continuity and Kirchhoff conditions at the interior vertex. We compute the multiplicity of the singular spectrum in terms of the spectral measures of the Weyl functions associated with the single (independently considered) boundary relations. This result is a generalization and refinement of a Theorem of I.S.Kac.

AB - We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schrödinger operator on a star-shaped graph with continuity and Kirchhoff conditions at the interior vertex. We compute the multiplicity of the singular spectrum in terms of the spectral measures of the Weyl functions associated with the single (independently considered) boundary relations. This result is a generalization and refinement of a Theorem of I.S.Kac.

KW - boundary relations

KW - Herglotz functions

KW - quantum graphs

KW - Schrödinger operators

KW - singular spectrum

KW - spectral multiplicity

KW - Weyl theory

UR - http://www.scopus.com/inward/record.url?scp=84897083547&partnerID=8YFLogxK

U2 - 10.1007/s00020-013-2106-9

DO - 10.1007/s00020-013-2106-9

M3 - Article

AN - SCOPUS:84897083547

VL - 78

SP - 523

EP - 575

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 4

ER -

ID: 9366278