多点散射体的传输特征值

Pub Date : 2021-08-18 DOI:10.32523/2306-6172-2021-9-4-17-25

P. Grinevich, R. A. O. Sciences, Moscow, Russia., L. I. F. T. Physics, Chernogolovka, Lomonosov Moscow State University, Cmap, Cnrs, 'Ecole polytechnique, I. P. Paris, Palaiseau, France.

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引用次数: 1

摘要

我们研究了Bethe-Pierls-Fermi-Zeldovich-Beresin-Faddeev型多点散射体在d=2和d=3维度上的透射本征值。我们证明了对于这些散射体：1）每个正能量E都是无限多重性的传输特征值（在强意义上）；2）每个复数E都是具有无限多重性的内部传输特征值。还讨论了尺寸d=1的情况。

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TRANSMISSION EIGENVALUES FOR MULTIPOINT SCATTERERS

We study the transmission eigenvalues for the multipoint scatterers of the Bethe- Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions d = 2 and d = 3. We show that for these scatterers: 1) each positive energy E is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex E is an interior transmission eigenvalue of infinite multiplicity. The case of dimension d = 1 is also discussed.

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