From: Brenda Cook (brenda@math.missouri.edu)
Date: Tue Sep 05 2006 - 08:38:16 CDT
SPECIAL PDE SEMINAR
University of Missouri-Columbia
Department of Mathematics
Slava Pivovarchik
South Ukrainian Pedagogical University
Odessa, Ukraine
Ambarzumyan’s Theorem on Graphs
Abstract: Ambarzumian’s theorem was the starting point of the
investigation of the inverse Sturm-Liouville problems. It deals with a
very exceptional case where one spectrum uniquely determines the
potential of the Sturm-Liouville equation on a finite interval.
Generally, as it was proved by Borg, one should know two spectra.
However, there exist some generalizations of Ambarzumian’s theorem (for
the vector Sturm-Liouville case, for the Dirac equation).
We consider the Sturm-Liouville equation on a star shaped graph with
Neumann boundary conditions at the pendant vertices and continuity
conditions and Kirkchoff’s condition at the central vertex and prove
analogues of Ambarzumian’s theorem.
Tuesday, September 5, 2006
3:00-3:50 p.m.
114 General Classroom Building
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