arXiv subjects
Publications and source records attributed to D. V. Puyda.
We prove the Bari-Markus property for spectral projectors of non-self-adjoint Dirac operators on a finite interval with square-integrable matrix-valued potentials and some separated boundary conditions.
We prove that there is a homeomorphism between the space of accelerants and the space of potentials of non-self-adjoint Dirac operators on a finite interval.
We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary conditions of the operator from its eigenvalues and suitably defined norming matrices.
We consider the direct and inverse spectral problems for Dirac operators on $(0,1)$ with matrix-valued potentials whose entries belong to $L_p(0,1)$, $p\in[1,\infty)$. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest a method for reconstructing the potential from the corresponding spectral data.
We consider the direct and inverse spectral problems for Dirac operators that are generated by the differential expressions $$ \mathfrak t_q:=\frac{1}{i}[I&0 0&-I]\frac{d}{dx}+[0&q q^*&0] $$ 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.