The Singular Inverse Sturm Liouville Problem,   Paul Sacks,   Iowa State University,  Wed, 22 April, 2009,   10:00 a.m. C-356


We consider inverse eigenvalue problems associated with the Sturm-Liouville operator
Alφ = −φ'' + (V(x) + l(l+1)/x^2 ) φ, 0 < x <1
with domain D(Al) suitably defined to incorporate boundary conditions. Here l is a nonnegative integer. In a typical problem one is given certain information about the eigenvalues and eigenfunctions of Al and seeks to determine the potential V. I will review some of the classical results in the regular (l=0) case, and then discuss some more recent work on the singular (l≥1) case.