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.
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Acknowledgements
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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Demirel-Frank, S. (2015). Spectral Inequalities for Quantum Graphs. In: Mugnolo, D. (eds) Mathematical Technology of Networks. Springer Proceedings in Mathematics & Statistics, vol 128. Springer, Cham. https://doi.org/10.1007/978-3-319-16619-3_6
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DOI: https://doi.org/10.1007/978-3-319-16619-3_6
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