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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Inverse Eigenvalue Problems on Directed Graphs


Author: Robert Carlson
Journal: Trans. Amer. Math. Soc. 351 (1999), 4069-4088
MSC (1991): Primary 34L05
Published electronically: July 1, 1999
MathSciNet review: 1473434
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Abstract: The differential operators $iD$ and $-D^2 - p$ are constructed on certain finite directed weighted graphs. Two types of inverse spectral problems are considered. First, information about the graph weights and boundary conditions is extracted from the spectrum of $-D^2$. Second, the compactness of isospectral sets for $-D^2 - p$ is established by computation of the residues of the zeta function.


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Additional Information

Robert Carlson
Affiliation: Department of Mathematics, University of Colorado at Colorado Springs, Colorado Springs, Colorado 80933
Email: carlson@vision.uccs.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02175-3
PII: S 0002-9947(99)02175-3
Keywords: Inverse eigenvalue problem, graph spectral theory, zeta function
Received by editor(s): May 13, 1996
Received by editor(s) in revised form: April 7, 1997
Published electronically: July 1, 1999
Article copyright: © Copyright 1999 American Mathematical Society