On the hot spots of quantum trees
classification
🧮 math.SP
math-phmath.MP
keywords
graphverticesattainsconditionsdegreediametereigenfunctionexample
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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 example where these vertices do not realise the diameter of the graph.
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