Geodesic
Quantum graphs with small edges: holomorphy of resolvents
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 498 (2021), pp. 21-26

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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.
Keywords: graph, small edge, resolvent, holomorphy in a small parameter. 
D. I. Borisov. Quantum graphs with small edges: holomorphy of resolvents. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 498 (2021), pp. 21-26. http://geodesic.mathdoc.fr/item/DANMA_2021_498_a3/
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     title = {Quantum graphs with small edges: holomorphy of resolvents},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {21--26},
     year = {2021},
     volume = {498},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_498_a3/}
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