Electron. J. Diff. Eqns., Vol. 2007(2007), No. 142, pp. 1-9.

Ambarzumian's theorem for trees

Robert Carlson, Vyacheslav Pivovarchik

The classical Ambarzumian's Theorem for Schrodinger operators $-D^2 + q$ on an interval, with Neumann conditions at the endpoints, says that if the spectrum of $(-D^2+q)$ is the same as the spectrum of $(-D^2)$ then $q=0$. This theorem is generalized to Schrodinger operators on metric trees with Neumann conditions at the boundary vertices.

Submitted April 12, 2007. Published October 24, 2007.
Math Subject Classifications: 34B45.
Key Words: Inverse eigenvalue problem; quantum graph.

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Robert Carlson
University of Colorado at Colorado Springs
Colorado Springs, CO 80933, USA
e-mail: carlson@uccs.edu
Vyacheslav Pivovarchik
South-Ukrainian State Pedagogical University
Staroportofrankovskaya Ul. 26, 65020 Odessa, Ukraine
email: v.pivovarchik@paco.net   vnp.@dtp.odessa.ua

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