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

Author
Von Below, J.; Lubary, J.; Vasseur, B.
Type of activity
Journal article
Journal
Results in mathematics
Date of publication
2013
Volume
63
Number
3
First page
1331
Last page
1350
DOI
https://doi.org/10.1007/s00025-012-0271-9 Open in new window
Project funding
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 Open in new window
Abstract
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...
Keywords
Laplacian, Liouville spaces, Locally infinite graphs and networks, eigenvalue multiplicities, harmonic functions
Group of research
EDP - Partial Differential Equations and Applications

Participants