SOME NEW INVERSE EIGENVALUE PROBLEMS

WILLIAM RUNDELL

rundell@math.tamu.edu

Department of Mathematics

Texas A&M University

College Station, TX 77843-3368, USA

Texas A&M University

College Station, TX 77843-3368, USA

We will look at two quite different problems to recover the potential in a second order differential operator from information on its spectrum. The first concerns the classical equation with (say) the boundary condition . At the other end point, . This problem has complex eigenvalues and we will show that a single such spectrum suffices to determine .

In the second problem we have the equation
with fixed conditions at and boundedness at . We examine the conjecture that two complete spectra
for
and for equals two distinct values , is sufficient to determine .

EPSRC Gregynog Workshop, 21-26 July 2002