Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 142, pp. 1-9.
Title: Ambarzumian's theorem for trees
Authors: Robert Carlson (Univ. of Colorado at Colorado Springs, USA)
Vyacheslav Pivovarchik (South-Ukrainian State Pedag. Univ., Ukraine)
Abstract:
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.