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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: 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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Additional Information

Pavel Kurasov
Affiliation: Department of Mathematics, LTH, Lund University, Box 118, 221 00 Lund, Sweden; Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden; and Department of Physics, St. Petersburg University, 198904 St. Peterhof, Russia
Email: kurasov@maths.lth.se, pak@math.su.se

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11077-3
PII: S 0002-9939(2011)11077-3
Received by editor(s): August 14, 2010
Received by editor(s) in revised form: February 15, 2011
Published electronically: October 26, 2011
Additional Notes: The author was supported in part by Swedish Research Council grant No. 50092501.
Communicated by: Hart F. Smith
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.