Faber-Krahn Type Inequalities for Trees

Türker Biyikoglu, Josef Leydold

Publication: Working/Discussion PaperWU Working Paper

Abstract

The Faber-Krahn theorem states that among all bounded domains with the same volume in Rn (with the standard Euclidean metric), a ball that has lowest first Dirichlet eigenvalue. Recently it has been shown that a similar result holds for (semi-)regular trees. In this article we show that such a theorem also hold for other classes of (not necessarily non-regular) trees. However, for these new results no couterparts in the world of the Laplace-Beltrami-operator on manifolds are known.
Original languageEnglish
Place of PublicationVienna
PublisherDepartment of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business
Publication statusPublished - 2003

Publication series

NamePreprint Series / Department of Applied Statistics and Data Processing
No.50

WU Working Paper Series

  • Preprint Series / Department of Applied Statistics and Data Processing

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