Spectral Theory of Infinite Quantum Graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F18%3A00496717" target="_blank" >RIV/61389005:_____/18:00496717 - isvavai.cz</a>

Alternative codes found

RIV/68407700:21340/18:00328114

Result on the web

<a href="http://dx.doi.org/10.1007/s00023-018-0728-9" target="_blank" >http://dx.doi.org/10.1007/s00023-018-0728-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00023-018-0728-9" target="_blank" >10.1007/s00023-018-0728-9</a>

Result language

angličtina

Original language name

Spectral Theory of Infinite Quantum Graphs

Original language description

We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a close connection between spectral properties of a quantum graph and the corresponding properties of a certain weighted discrete Laplacian on the underlying discrete graph. Using this connection together with spectral theory of (unbounded) discrete Laplacians on infinite graphs, we prove a number of new results on spectral properties of quantum graphs. Namely, we prove several self-adjointness results including a Gaffney-type theorem. We investigate the problem of lower semiboundedness, prove several spectral estimates (bounds for the bottom of spectra and essential spectra of quantum graphs, CLR-type estimates) and study spectral types.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Project

<a href="/en/project/GA17-01706S" target="_blank" >GA17-01706S: Mathematical-Physics Models of Novel Materials</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Annales Henri Poincare

ISSN

1424-0637

e-ISSN

—

Volume of the periodical

19

Issue of the periodical within the volume

11

Country of publishing house

CH - SWITZERLAND

Number of pages

54

Pages from-to

3457-3510

UT code for WoS article

000448591700007

EID of the result in the Scopus database

2-s2.0-85055704636