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Contemporary Mathematics
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SYSNO ASEP 0500202 Document Type M - Monograph Chapter R&D Document Type Monograph Chapter Title Optimization of the lowest eigenvalue for leaky star graphs Author(s) Exner, Pavel (UJF-V) RID, ORCID, SAI
Lotoreichik, Vladimir (UJF-V) ORCID, SAINumber of authors 2 Source Title Contemporary Mathematics, Mathematical Problems in Quantum Physics, 717. - Atlanta : American Mathematical Society, 2018 - ISSN 0271-4132 - ISBN 978-1-4704-3681-0 Pages s. 187-196 Number of pages 11 s. Number of copy 250 Number of pages 350 Publication form Print - P Language eng - English Country US - United States Keywords Eigenvalues ; mathematical models ; Eigenfunctions Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA17-01706S GA ČR - Czech Science Foundation (CSF) Institutional support UJF-V - RVO:61389005 UT WOS 000465195200012 EID SCOPUS 85059753919 DOI 10.1090/conm/717/14448 Annotation We consider the problem of geometric optimization for the lowest eigenvalue of the two-imensional Schrödinger operator with an attractive delta-interaction of a fixed strength, the support of which is a star graph with finitely many edges of an equal length is in the interval from 0 to 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2019
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