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Optimization of the lowest eigenvalue for leaky star graphs

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F18%3A00346535" target="_blank" >RIV/68407700:21340/18:00346535 - isvavai.cz</a>

  • Result on the web

    <a href="https://doi.org/10.1090/conm/717/14448" target="_blank" >https://doi.org/10.1090/conm/717/14448</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1090/conm/717/14448" target="_blank" >10.1090/conm/717/14448</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Optimization of the lowest eigenvalue for leaky star graphs

  • Original language description

    We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schriidinger operator with an attractive (5 interaction of a fixed strength, the support of which is a star graph with finitely many edges of an equal length L is an element of (0, infinity]. Under the constraint of fixed number of the edges and fixed length of them, we prove that the lowest eigenvalue is maximized by the fully symmetric star graph. The proof relies on the Birman-Schwinger principle, properties of the Macdonald function, and on a geometric inequality for polygons circumscribed into the unit circle.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

    10100 - Mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2018

  • Confidentiality

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

Data specific for result type

  • Article name in the collection

    MATHEMATICAL PROBLEMS IN QUANTUM PHYSICS

  • ISBN

    978-1-4704-3681-0

  • ISSN

    0271-4132

  • e-ISSN

    1098-3627

  • Number of pages

    10

  • Pages from-to

    187-196

  • Publisher name

    American Mathematical Society

  • Place of publication

    Providence

  • Event location

    Georgia Inst Technol, Atlanta, GA

  • Event date

    Oct 8, 2016

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article

    000465195200012