Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum

DOI10.13108/2019-11-2-56zbMath1463.34127OpenAlexW2964014030WikidataQ127459013 ScholiaQ127459013MaRDI QIDQ5137831

M. N. Konyrkulzhaeva, Denis I. Borisov

Publication date: 2 December 2020

Published in: Ufimskii Matematicheskii Zhurnal (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/ufa471

zbMATH Keywords

graphasymptoticsspectrumsmall edge

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (5)

Resolvent of a Schrödinger operator on a model graph with small loops ⋮ On a model graph with a loop and small edges. Holomorphy property of resolvent ⋮ On discrete spectrum of a model graph with loop and small edges ⋮ Quantum graphs with small edges: holomorphy of resolvents ⋮ Analyticity of resolvents of elliptic operators on quantum graphs with small edges

Cites Work

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• The norm resolvent convergence for elliptic operators in multi-dimensional domains with small holes
• Approximation of a general singular vertex coupling in quantum graphs
• On a \(\mathcal{PT}\)-symmetric waveguide with a pair of small holes
• ASYMPTOTIC EXPANSIONS OF THE EIGENVALUES OF BOUNDARY VALUE PROBLEMS FOR THE LAPLACE OPERATOR IN DOMAINS WITH SMALL HOLES

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