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تسجيل مستخدم جديدSimplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph
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We prove that after an arbitrarily small adjustment of edge lengths, the spectrum of a compact quantum graph with $delta$-type vertex conditions can be simple. We also show that the eigenfunctions, with the exception of those living entirely on a looping edge, can be made to be non-vanishing on all vertices of the graph. As an application of the above result, we establish that the secular manifold (also called determinant manifold) of a large family of graphs has exactly two smooth connected components.
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