半格上周期Jacobi算子的摄动
Periodic Jacobi operator with finitely supported perturbation on the half-lattice
摘要：
我们考虑半格上周期Jacobi算子$J$的扰动.我们描述了$J$的所有本征值和共振，并给出了它们的性质。我们解决的逆共振问题：我们证明，从支撑扰动的Jost函数的映射是一对一的，到上，我们展示了如何Jost函数可以重建的特征值，共振和一组零的$S(ł)-1,$，其中$S(ł)$是散射矩阵。
英文摘要：
We consider the periodic Jacobi operator $J$ with finitely supported perturbations on the half-lattice. We describe all eigenvalues and resonances of $J$ and give their properties. We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the Jost functions is one-to-one and onto, we show how the Jost functions can be reconstructed from the eigenvalues, resonances and the set of zeros of $S(ł)-1,$ where $S(ł)$ is the scattering matrix.
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