School of Mathematics
University of the Witwatersrand
Private Bag 3, P O WITS 2050, South Africa
email: scurrie@ananzi.co.za
School of Mathematics
University of the Witwatersrand
Private Bag 3, P O WITS 2050, South Africa
bwatson@maths.wits.ac.za
Sonja Currie, Bruce A. Watson
Abstract:
We consider the spectral structure of second order boundary-value
problems on graphs. A variational formulation for boundary-value
problems on graphs is given. As a consequence we can formulate an
analogue of Dirichlet-Neumann bracketing for boundary-value
problems on graphs. This in turn gives rise to eigenvalue and
eigenfunction asymptotic approximations.
Submitted March 9, 2005. Published August 24, 2005.
Math Subject Classifications: 47E05, 34L20, 34B45.
Key Words: Differential operators; spectrum; graphs.
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Sonja Currie School of Mathematics University of the Witwatersrand Private Bag 3, P O WITS 2050, South Africa email: scurrie@ananzi.co.za |
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Bruce A. Watson School of Mathematics University of the Witwatersrand Private Bag 3, P O WITS 2050, South Africa bwatson@maths.wits.ac.za |
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