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

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

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

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database

  • CEP classification

  • OECD FORD branch

    10102 - Applied mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2019

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Journal of mathematical sciences

  • ISSN

    1072-3374

  • e-ISSN

  • Volume of the periodical

    239

  • Issue of the periodical within the volume

    3

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    20

  • Pages from-to

    248-267

  • UT code for WoS article

  • EID of the result in the Scopus database

    2-s2.0-85065441718