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A STRUCTURED INVERSE SPECTRUM PROBLEM FOR INFINITE GRAPHS AND UNBOUNDED OPERATORS
Part of
EHSSAN KHANMOHAMMADI
Journal:

Bulletin of the Australian Mathematical Society / Volume 98 / Issue 3 / December 2018

Published online by Cambridge University Press:

15 August 2018, pp. 363-371

Print publication:

December 2018
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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 $\unicode[STIX]{x1D6EC}$.