Exterior–interior duality for discrete graphs

Smilansky, Uzy 2009. Exterior–interior duality for discrete graphs. Journal of Physics A: Mathematical and Theoretical 42 (3) , 035101. 10.1088/1751-8113/42/3/035101

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Abstract

The exterior–interior duality expresses a deep connection between the Laplace spectrum in bounded and connected domains in R squared, and the scattering matrices in the exterior of the domains. Here, this link is extended to the study of the spectrum of the discrete Laplacian on finite graphs. For this purpose, two methods are devised for associating scattering matrices to the graphs. The exterior–interior duality is derived for both methods.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	IOP Publishing
ISSN:	1751-8121
Last Modified:	19 Mar 2016 22:24
URI:	https://orca.cardiff.ac.uk/id/eprint/15158

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