Abstract
We consider a general scalar self-adjoint elliptic second order operator with general boundary conditions on an arbitrary metric graph containing a subgraph with edges of lengths proportional to a small parameter. We show that the resolvent of such operator is holomorphic in the small parameter and provide its representations by Taylor series. The coefficients of the series are found rather explicitly.
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Funding
This work was supported by the Russian Science Foundation, project no. 20-11-19995.
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Translated by I. Ruzanova
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Borisov, D.I. Quantum Graphs with Small Edges: Holomorphy of Resolvents. Dokl. Math. 103, 113–117 (2021). https://doi.org/10.1134/S1064562421030054
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DOI: https://doi.org/10.1134/S1064562421030054