Abstract
In this paper, we study the generation problem of Riesz basis for a general network of strings with joint damping at each vertex. First, we give a basic spectral property of the system operator \( \mathcal{A} \). Under certain conditions, we prove that the spectrum of \( \mathcal{A} \) is distributed in a strip parallel to the imaginary axis. By the discussion of the completeness of generalized eigenvectors of the operator \( \mathcal{A} \), we prove further that there exists a sequence of generalized eigenvectors of \( \mathcal{A} \) that forms a Riesz basis with parentheses in the Hilbert state space.
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This research is supported by the Natural Science Foundation of China grant NSFC-60874034.
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Ni Guo, Y., Qi Xu, G. Stability and Riesz basis property for general network of strings. J Dyn Control Syst 15, 223–245 (2009). https://doi.org/10.1007/s10883-009-9064-1
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DOI: https://doi.org/10.1007/s10883-009-9064-1