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A STRUCTURED INVERSE SPECTRUM PROBLEM FOR INFINITE GRAPHS AND UNBOUNDED OPERATORS

Part of: Graph theory General theory of linear operators Basic linear algebra

Published online by Cambridge University Press:  15 August 2018

EHSSAN KHANMOHAMMADI Open the ORCID record for EHSSAN KHANMOHAMMADI [Opens in a new window]
EHSSAN KHANMOHAMMADI*
Affiliation:
Lancaster, PA 17603, USA email [email protected]
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Abstract

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Let $G$ be an infinite graph on countably many vertices and let $\unicode[STIX]{x1D6EC}$ be a closed, infinite set of real numbers. We establish the existence of an unbounded self-adjoint operator whose graph is $G$ and whose spectrum is $\unicode[STIX]{x1D6EC}$.

Keywords

inverse spectrum probleminfinite graphisospectralunbounded operator

MSC classification

Primary: 05C63: Infinite graphs
Secondary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.) 15A29: Inverse problems 47A10: Spectrum, resolvent
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 3 , December 2018 , pp. 363 - 371
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

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Schmüdgen, K., Unbounded Self-adjoint Operators on Hilbert Space, Graduate Texts in Mathematics, 265 (Springer, Dordrecht, 2012).Google Scholar