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)