DMS Applied Mathematics Seminar

Speaker: Stephen Shipman,  Louisiana State University (LSU)

Title: Inverse problem for a spectral asymmetry function

Abstract: For the Schrödinger equation $−u'' + q(x)u = λu$ on a finite x-interval, there is defined an “asymmetry function” $a(λ;q)$, which is entire of order 1/2 and type 1 in $λ$.  The main result identifies the classes of square-integrable potentials $q(x)$ that possess a common asymmetry function.  For any given $a(λ)$, there is one potential for each Dirichlet spectral sequence.  This has applications to the spectral theory of multi-layer quantum graphs.  (Collaboration with Malcolm Brown, Karl Michael Schmidt, and Ian Wood)