Inverse spectral problems for Dirac operators on a finite interval

Details Inverse spectral problems for Dirac operators on a finite interval Inverse spectral problems for Dirac operators on a finite interval

2011-01-12

arxiv.org/abs/1101.2302v1

Mathematics

Functional Analysis

30 pages

Scientific paper

We consider the direct and inverse spectral problems for Dirac operators that are generated by the differential expressions $$ \mathfrak t_q:=\frac{1}{i}\begin{pmatrix}I&0 0&-I\end{pmatrix}\frac{d}{dx}+\begin{pmatrix}0&q q^*&0\end{pmatrix} $$ and some separated boundary conditions. Here $q$ is an $r\times r$ matrix-valued function with entries belonging to $L_2((0,1),\mathbb C)$ and $I$ is the identity $r\times r$ matrix. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest an algorithm of reconstructing the potential $q$ from the corresponding spectral data.

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