Bounds on the first non-null eigenvalue for self-adjoint boundary value problems on networks

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Title:	Bounds on the first non-null eigenvalue for self-adjoint boundary value problems on networks
Author:	Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. VARIDIS - Varietats Riemannianes Discretes i Teoria del Potencial
Abstract:	We aim here at obtaining bounds on the first non-null eigenvalue for self-adjoint boundary value problems on a weighted network by means of equilibrium measures, that includes the study of Dirichlet, Neumann and Mixed problems. We also show the sharpness of these bounds throughout the analysis of some known examples. In particular, we emphasize the case of distance-regular graphs, and we show that the bounds obtained are better than the known until now.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta -Discrete mathematics -Boundary value problems -Eigenvalues -Networks -Self-adjoint eigenvalue problems -Discrete laplacian -Equilibrium measures -Distance-regular graphs -Matemàtica discreta -Xarxes de comunicacions -- Matemàtica -Valors propis -Classificació AMS::34 Ordinary differential equations::34B Boundary value problems {For ordinary differential operators, see 34Lxx}
Rights:	Attribution-NonCommercial-NoDerivs 2.5 Spain http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Document type:	Article
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