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.