|
This article is cited in 3 scientific papers (total in 3 papers)
MATHEMATICS
Quantum graphs with small edges: holomorphy of resolvents
D. I. Borisovabc a Institute of Mathematics, Ufa Federal Research Center, Russian Academy of Sciences, Ufa, Russia
b Bashkir State Pedagogical University, Ufa, Russia
c University of Hradec Králové, Czech Republic
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.
Keywords:
graph, small edge, resolvent, holomorphy in a small parameter.
Citation:
D. I. Borisov, “Quantum graphs with small edges: holomorphy of resolvents”, Dokl. RAN. Math. Inf. Proc. Upr., 498 (2021), 21–26; Dokl. Math., 103:3 (2021), 113–117
Linking options:
https://www.mathnet.ru/eng/danma171 https://www.mathnet.ru/eng/danma/v498/p21
|
Statistics & downloads: |
Abstract page: | 77 | Full-text PDF : | 18 | References: | 12 |
|