Quantum graphs with small edges: holomorphy of resolvents

DOI10.1134/S1064562421030054zbMath1479.81026OpenAlexW3196558040MaRDI QIDQ2243865

Denis I. Borisov

Publication date: 11 November 2021

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562421030054

zbMATH Keywords

resolventgraphsmall edgeholomorphy in small parameter

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Distance in graphs (05C12) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (2)

Resolvent of a Schrödinger operator on a model graph with small loops ⋮ On discrete spectrum of a model graph with loop and small edges

Cites Work

• Unnamed Item
• On the frequency spectrum of a multidimensional analogue of a fabric membrane
• On a model graph with a loop and small edges. Holomorphy property of resolvent
• Limits of quantum graph operators with shrinking edges
• Scale invariant effective Hamiltonians for a graph with a small compact core
• Approximation of a general singular vertex coupling in quantum graphs
• Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum

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