65 citations · 295 across the 21 of their papers we have counts for
4 papers · 1 filter
On the hot spots of quantum trees
James Kennedy, Jonathan Rohleder
We show that any second eigenfunction of the Laplacian with standard vertex conditions on a metric tree graph attains its extremal values only at degree one vertices, and give an e…
A family of diameter-based eigenvalue bounds for quantum graphs
J. B. Kennedy
We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in…
Surgery principles for the spectral analysis of quantum graphs
Gregory Berkolaiko, James B. Kennedy, Pavel Kurasov +1
We present a systematic collection of spectral surgery principles for the Laplacian on a metric graph with any of the usual vertex conditions (natural, Dirichlet or -type), whic…
Extremal domains and Pólya-type inequalities for the Robin Laplacian on rectangles and unions of rectangles
Pedro Freitas, James Kennedy
We show that eigenvalues of the Robin Laplacian with a positive boundary parameter on rectangles and unions of rectangtes satisfy Pólya-type inequalities, albeit with an expone…