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Published 2015 | Version public
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Spectral Inequalities for Quantum Graphs

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Abstract

We review our joint work with Evans Harrell on semiclassical and universal inequalities for quantum graphs. The proofs of these inequalities are based on an abstract trace inequality for commutators of operators. In this article we give a new proof of this abstract trace inequality. Another ingredient in proving semiclassical and universal inequalities is an appropriate choice of operators in this trace inequality. We provide a new approximation method for such a choice.

Additional Information

© 2015 Springer International Publishing Switzerland. The author is grateful to Evans Harrell with whom the results reviewed in Sect. 2 were obtained and to Timo Weidl who suggested that there might be an alternative proof of the trace inequality. Many thanks to Delio Mugnolo for organizing the wonderful conference "Mathematical Technology of Networks".

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Eprint ID
63135
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CaltechAUTHORS:20151222-103336784

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Created
2015-12-22
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Updated
2021-11-10
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Mathematics Department
Series Name
Springer Proceedings in Mathematics & Statistics
Series Volume or Issue Number
128