具有非局部匹配条件的星形图上微分算子的反问题
Inverse problem for a differential operator on a star-shaped graph with nonlocal matching condition
摘要：
本文研究了度量图上一类新的非局部算子的逆谱问题。研究了星形图上具有非局部积分匹配条件的Laplace微分算子。这个算子是伴随的功能微分算子与冻结的论点，在中央顶点的图。我们研究的逆问题，包括在恢复的积分条件系数的特征值。我们得到的频谱特征，重建算法，并证明了反问题的解的唯一性。
英文摘要：
In this paper, we develop two approaches to investigation of inverse spectral problems for a new class of nonlocal operators on metric graphs. The Laplace differential operator is considered on a star-shaped graph with nonlocal integral matching condition. This operator is adjoint to the functional-differential operator with frozen argument at the central vertex of the graph. We study the inverse problem that consists in the recovery of the integral condition coefficients from the eigenvalues. We obtain the spectrum characterization, reconstruction algorithms, and prove the uniqueness of the inverse problem solution.
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