论文标题
持续延迟的狄拉克操作员的反问题：独特性，表征，统一稳定性
Inverse problems for Dirac operators with constant delay: uniqueness, characterization, uniform stability
论文作者
论文摘要
我们启动研究以持续延迟的Dirac-type功能分化算子的逆频谱问题。为简单起见，我们将自己限制在延迟参数不少于间隔的一半的情况下。但是，对于被考虑的情况，我们回答了反频谱理论中通常提出的各种问题。具体而言，从一个具有一个常见边界条件的两个边界价值问题的完整光谱或两个边界值问题的物质中研究了两个复杂$ L_2 $ - 电位的重建。我们为物质提供了必要和足够的条件，足以实现电势的独特确定。此外，获得了两种反问题的可溶性的必要条件。对于涉及完整光谱的逆问题，我们在每个球中也建立了均匀的稳定性。为此，我们使用了最新的结果，即具有渐近型功能的均匀稳定性具有渐近分离的零。
We initiate studying inverse spectral problems for Dirac-type functional-differential operators with constant delay. For simplicity, we restrict ourselves to the case when the delay parameter is not less than one half of the interval. For the considered case, however, we give answers to the full range of questions usually raised in the inverse spectral theory. Specifically, reconstruction of two complex $L_2$-potentials is studied from either complete spectra or subspectra of two boundary value problems with one common boundary condition. We give conditions on the subspectra that are necessary and sufficient for the unique determination of the potentials. Moreover, necessary and sufficient conditions for the solvability of both inverse problems are obtained. For the inverse problem involving the complete spectra, we establish also uniform stability in each ball. For this purpose, we use recent results on uniform stability of sine-type functions with asymptotically separated zeros.
