Inverse Scattering Problem for a Special Class of Canonical Systems and Non-linear Fourier Integral. Part I: Asymptotics of Eigenfunctions
Inverse Scattering Problem for a Special Class of Canonical Systems and Non-linear Fourier Integral. Part I: Asymptotics of Eigenfunctions
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一类特殊典型系统和非线性傅立叶积分的逆散射问题。
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
P. Yuditskii
中科院分区：
文献类型：
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作者：
S. Kupin;F. Peherstorfer;A. Volberg;P. Yuditskii
最近在[20]中提出了一种新颖的Jacobi矩阵逆散射方法。作者考虑了相当复杂的谱集（包括正勒贝格测度的康托集），但他们没有考虑质量点谱。本文对半轴上绝对连续谱和负半轴上纯点谱满足Blaschke条件的连续情形，也给出了类似的结论。这导致我们的解决方案的逆散射问题的一类典型的系统，推广的情况下Sturm-Liouville（薛定谔）运营商。
An original approach to the inverse scattering for Jacobi matrices was recently suggested in [20]. The authors considered quite sophisticated spectral sets (including Cantor sets of positive Lebesgue measure), however they did not take into account the mass point spectrum. This paper follows similar lines for the continuous setting with an absolutely continuous spectrum on the half-axis and a pure point spectrum on the negative half-axis satisfying the Blaschke condition. This leads us to the solution of the inverse scattering problem for a class of canonical systems that generalizes the case of Sturm-Liouville (Schrodinger) operator.