Weyl-Titchmarsh Functions of Vector-Valued Sturm-Liouville Operators on the Unit Interval

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Date
2008MFO Scientific Program
OWLF 2008Series
Oberwolfach Preprints;2008,13Author
Chelkak, Dmitry
Korotyaev, Evgeny
Metadata
Show full item recordOWP-2008-13
Abstract
The matrix-valued Weyl-Titchmarsh functions $M(\lambda)$ of vector-valued Sturm-Liouville operators on the unit interval with the Dirichlet boundary conditions are considered. The collection of the eigenvalues (i.e., poles of $M(\lambda)$) and the residues of $M(\lambda)$ is called the spectral data of the operator. The complete characterization of spectral data (or, equivalently, $N \times N$ Weyl-Titchmarsh functions) corresponding to $N \times N$ self-adjoint square-integrable matrix-valued potentials is given, if all $N$ eigenvalues of the averaged potential are distinct.