Eigenvalue asymptotics for differential operators on graphs

Authors:
Sonja Currie;Bruce A. Watson
Affiliations:
School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa;School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 1
Cited 1

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Abstract

We consider the spectral structure for differential equations on graphs. In particular, we show that self-adjointness does not necessarily imply regularity, we also show that the algebraic and geometric eigenvalue multiplicities of formally self-adjoint differential operators on graphs are equal. Asymptotic bounds for the eigenvalues are then found.