Spectral Multiplicity of Selfadjoint Schrödinger Operators on Star-Graphs with Standard Interface Conditions
Spectral Multiplicity of Selfadjoint Schrödinger Operators on Star-Graphs with Standard Interface Conditions
复制标题
标准接口条件星图上自伴薛定谔算子的谱重数
DOI：
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复制
发表时间：
2012
影响因子：
0.8
通讯作者：
H. Woracek
中科院分区：
文献类型：
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作者：
S. Simonov;H. Woracek
我们分析了自伴算子的奇异谱，这种奇异谱是由有限个边界关系与标准的界面条件相粘而产生的。这种情况的一个模型例子是在一个星形图上的薛定谔算子，该星形图在内部顶点具有连续性和基尔霍夫条件。我们计算的奇异谱的Weyl函数与单一的（独立考虑）边界关系的谱措施方面的多重性。这个结果是I.S.Kac的一个定理的推广和改进。
We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schrödinger operator on a star-shaped graph with continuity and Kirchhoff conditions at the interior vertex. We compute the multiplicity of the singular spectrum in terms of the spectral measures of the Weyl functions associated with the single (independently considered) boundary relations. This result is a generalization and refinement of a Theorem of I.S.Kac.