Spectral Theory of Infinite Quantum Graphs

Kód výsledku v IS VaVaI

RIV/61389005:_____/18:00496717 - isvavai.cz

Nalezeny alternativní kódy

RIV/68407700:21340/18:00328114

Výsledek na webu

http://dx.doi.org/10.1007/s00023-018-0728-9

DOI - Digital Object Identifier

10.1007/s00023-018-0728-9

Jazyk výsledku

angličtina

Název v původním jazyce

Spectral Theory of Infinite Quantum Graphs

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Spectral Theory of Infinite Quantum Graphs

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

GA17-01706S: Matematicko-fyzikální modely nových materiálů

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Annales Henri Poincare

ISSN

1424-0637

e-ISSN

—

Svazek periodika

19

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

54

Strana od-do

3457-3510

Kód UT WoS článku

000448591700007

EID výsledku v databázi Scopus

2-s2.0-85055704636