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## Eigenvalue multiplicities for second order elliptic operators on networks

Author
Von Below, J.; Lubary, J.
Type of activity
Journal article
Journal
Operators and Matrices
Date of publication
2013-09
Volume
7
Number
3
First page
587
Last page
602
DOI
https://doi.org/10.7153/oam-07-32
Project funding
ECUACIONES EN DERIVADAS PARCIALES; ANÁLISIS Y APLICACIONES
Abstract
We present some general bounds for the algebraic and geometric multiplicity of eigenvalues of second order elliptic operators on finite networks under continuity and weighted Kirchhoff flow conditions at the vertices. In particular the algebraic multiplicity of an eigenvalue is shown to be strictly bounded from above by the number of vertices if there are no eigenfunctions vanishing in all nodes, and to be bounded from above by the number of edges if there are such eigenfunctions.
Keywords
Elliptic operators on networks, adjacency and transition operators, eigenvalue multiplicities
Group of research
EDP - Partial Differential Equations and Applications