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arXiv · 2212.03820

Spectral multiplicity of selfadjoint Schroedinger operators on star-graphs with general interface conditions

Sergey Simonov·Harald Woracek
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Abstract

We consider selfadjoint operators obtained by pasting a finite number of boundary relations with one-dimensional boundary space. A typical example of such an operator is the Schr\"odinger operator on a star-graph with a finite number of finite or infinite edges and an interface condition at the common vertex. A wide class of "selfadjoint" interface conditions, subject to a assumption which is generically satisfied, is considered. We investigate properties of spectral multiplicity of singular spectrum (continuous as well as point) in terms of the spectral data of decoupled operators.

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Sergey Simonov, Harald Woracek. 2022-12-07. Spectral multiplicity of selfadjoint Schroedinger operators on star-graphs with general interface conditions. https://arxiv.org/abs/2212.03820

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