We establish an upper bound on the spectral gap for compact quantum graphs which depends only on the diameter and total number of vertices. This bound is asymptotically sharp for pumpkin chains with number of edges tending to infinity.
Borthwick, D., Corsi, L., Jones, K. (2021). Sharp diameter bound on the spectral gap for quantum graphs. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 149(7), 2879-2890 [10.1090/proc/15090].
Sharp diameter bound on the spectral gap for quantum graphs
Corsi L.;
2021-01-01
Abstract
We establish an upper bound on the spectral gap for compact quantum graphs which depends only on the diameter and total number of vertices. This bound is asymptotically sharp for pumpkin chains with number of edges tending to infinity.File in questo prodotto:
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