Evgeny Korotyaev – Inverse Problems for vector-valued Sturm-Liouville Operators on the Unit Interval Quand 23 juin 2010 Ajouter au Calendrier Télécharger ICS Calendrier Google iCalendar Office 365 Outlook Live Abstract. We consider the inverse problem for the Schr odinger operator $Hy = ?y?? + V y$ on the unit interval $[0, 1]$ with the Dirichlet boundary condition $ y(1) = y(1)=0$. Here $y=(y_j)_1^N, N >3 $ is a vector-valued function and $V =V(x)$ is a $N \times N$ matrix valued self-adjoint potential from $L^2 (0,1)$. The collection of the eigenvalues of $H$ and some subspaces (associated with eigenvalues) is called the spectral data of the operator. The complete characterization of spectral data corresponding to $N \times N$ self-adjoint square-integrable matrix-valued potentials is given. Moreover, for any $V$ we describe the so-called iso-spectral set, i.e., the set of all potentials with the same spectrum of the corresponding the Schrödinger operator. The talk is a joint with Dmitri Chelkak and is based on the papers 1) Chelkak, Dmitri; Korotyaev, Evgeny Weyl-Titchmarsh functions of vector-valued Sturm-Liouville operators on the unit interval, Jour. Func. Anal., 257 (2009), 1546- 1588. 2) Chelkak, D.; Korotyaev, E. Parametrization of the isospectral set for the vector- valued Sturm-Liouville problem, J. Funct. Anal., 241(2006), 359-373.
