Spectral theory for nonconservative transmission line networks

Robert Carlson

doi:10.3934/nhm.2011.6.257

Article Contents

2011, Volume 6, Issue 2: 257-277. Doi: 10.3934/nhm.2011.6.257

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Spectral theory for nonconservative transmission line networks

Robert Carlson^1,

1.
Department of Mathematics, University of Colorado at Colorado Springs, Colorado Springs, CO 80933

Received: July 31, 2010

Revised: March 31, 2011

Published: May 2011

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Abstract

The global theory of transmission line networks with nonconservative junction conditions is developed from a spectral theoretic viewpoint. The rather general junction conditions lead to spectral problems for nonnormal operators. The theory of analytic functions which are almost periodic in a strip is used to establish the existence of an infinite sequence of eigenvalues and the completeness of generalized eigenfunctions. Simple eigenvalues are generic. The asymptotic behavior of an eigenvalue counting function is determined. Specialized results are developed for rational graphs.

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Mathematics Subject Classification: Primary: 34B45.

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