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Can one distinguish quantum trees from the boundary?

Author: Pavel Kurasov
Journal: Proc. Amer. Math. Soc. 140 (2012), 2347-2356
MSC (2010): Primary 34L25, 81U40; Secondary 35P25, 81V99
Posted: October 26, 2011
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Abstract: Schrödinger operators on metric trees are considered. It is proven that for certain matching conditions the Titchmarsh-Weyl matrix function does not determine the underlying metric tree; i.e. there exist quantum trees with equal Titchmarsh-Weyl functions. The constructed trees form one-parameter families of isospectral and isoscattering graphs.

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