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Some remarks on the eigenvalue multiplicities of the Laplacian on infinite locally finite trees

Autor
Von Below, J.; Lubary, J.; Vasseur, B.
Tipus d'activitat
Article en revista
Revista
Results in mathematics
Data de publicació
2013
Volum
63
Número
3
Pàgina inicial
1331
Pàgina final
1350
DOI
https://doi.org/10.1007/s00025-012-0271-9 Obrir en finestra nova
Projecte finançador
Ecuaciones en derivadas parciales: problemas de reacción-difusión y problemas geométricos
URL
http://link.springer.com.recursos.biblioteca.upc.edu/article/10.1007/s00025-012-0271-9 Obrir en finestra nova
Resum
We consider the continuous Laplacian on an infinite uniformly locally finite network under natural transition conditions as continuity at the ramification nodes and the classical Kirchhoff flow condition at all vertices in a L8-setting. The characterization of eigenvalues of infinite multiplicity for trees with finitely many boundary vertices (von Below and Lubary, Results Math 47:199–225, 2005, 8.6) is generalized to the case of infinitely many boundary vertices. Moreover, it is shown that on...
Paraules clau
Laplacian, Liouville spaces, Locally infinite graphs and networks, eigenvalue multiplicities, harmonic functions
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

Participants