二阶块算子矩阵的谱浓度和共振及相关的λ有理Sturm-Liouville问题

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-12-08 DOI:10.1098/rspa.2003.1272

B. M. Brown, M. Langer, M. Marletta

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引用次数: 5

摘要

本文研究了L2(0,1)⊕L2(0,1)空间中块算子矩阵(- d2 d x 2 +q tw tw)的谱集中共振点和谱集中点。特别地，我们研究了共振/特征值λ(t)的动力学，表明嵌入的特征值可以演变成共振，并且被本质谱吸收的特征值产生共振点。在共振和谱集中点之间也建立了联系。最后给出了一些数值算例，表明上述每种理论可能性都是可以实现的。

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Spectral concentrations and resonances of a second–order block operator matrix and an associated λ–rational Sturm-Liouville problem

This paper studies the resonances and points of spectral concentration of the block operator matrix ( − d2 d x 2 +q tw tw ) in the space L2(0,1)⊕L2(0,1). In particular we study the dynamics of the resonance/eigenvalue λ(t), showing that an embedded eigenvalue can evolve into a resonance and that eigenvalues which are absorbed by the essential spectrum give rise to resonance points. A connection is also established between resonances and points of spectral concentration. Finally, some numerical examples are given which show that each of the above theoretical possibilities can be realized.

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Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences

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