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Eigenvalue multiplicities for second order elliptic operators on networks

Autor
Von Below, J.; Lubary, J.
Tipus d'activitat
Article en revista
Revista
Operators and Matrices
Data de publicació
2013-09
Volum
7
Número
3
Pàgina inicial
587
Pàgina final
602
DOI
https://doi.org/10.7153/oam-07-32 Obrir en finestra nova
Projecte finançador
ECUACIONES EN DERIVADAS PARCIALES; ANÁLISIS Y APLICACIONES
Resum
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.
Paraules clau
Elliptic operators on networks, adjacency and transition operators, eigenvalue multiplicities
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

Participants