Perturbation of Threshold of the Essential Spectrum of the Schrödinger Operator on the Simplest Graph with a Small Edge

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F19%3A50016364" target="_blank" >RIV/62690094:18470/19:50016364 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/content/pdf/10.1007%2Fs10958-019-04302-0.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007%2Fs10958-019-04302-0.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10958-019-04302-0" target="_blank" >10.1007/s10958-019-04302-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Perturbation of Threshold of the Essential Spectrum of the Schrödinger Operator on the Simplest Graph with a Small Edge

Popis výsledku v původním jazyce

On a star graph consisting of two infinite edges and one small edge, we consider the Schrödinger operators with piecewise-constant potentials on the infinite edges and with a singular potential on the small edge respectively. A δ′-interaction is given at the interior vertex of the graph, and the Dirichlet or Neumann condition is imposed at the boundary vertex of the small edge. We determine the limit boundary conditions, obtain two-term asymptotics for the resolvents in the operator norm and error estimates. The phenomenon of isolated eigenvalues emerging from the threshold of the essential spectrum is discussed. We establish efficient and easily verified sufficient conditions for the existence or absence of such eigenvalues. We establish the holomorphic dependence of the appeared eigenvalues on the edge length and write explicitly the first terms of the Taylor expansions of such eigenvalues.

Název v anglickém jazyce

Perturbation of Threshold of the Essential Spectrum of the Schrödinger Operator on the Simplest Graph with a Small Edge

Popis výsledku anglicky

On a star graph consisting of two infinite edges and one small edge, we consider the Schrödinger operators with piecewise-constant potentials on the infinite edges and with a singular potential on the small edge respectively. A δ′-interaction is given at the interior vertex of the graph, and the Dirichlet or Neumann condition is imposed at the boundary vertex of the small edge. We determine the limit boundary conditions, obtain two-term asymptotics for the resolvents in the operator norm and error estimates. The phenomenon of isolated eigenvalues emerging from the threshold of the essential spectrum is discussed. We establish efficient and easily verified sufficient conditions for the existence or absence of such eigenvalues. We establish the holomorphic dependence of the appeared eigenvalues on the edge length and write explicitly the first terms of the Taylor expansions of such eigenvalues.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Journal of mathematical sciences

ISSN

1072-3374

e-ISSN

—

Svazek periodika

239

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

248-267

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85065441718