Bounds on the negative eigenvalues of Laplacians on finite metric graphs

DOI10.1007/s00020-013-2064-2zbMath1277.34031arXiv1211.4139OpenAlexW2024383197MaRDI QIDQ2391796

Amru Hussein

Publication date: 5 August 2013

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.4139

zbMATH Keywords

Poincaré-type inequalitiesdifferential operators on metric graphslower bounds on the spectrumnegative eigenvalues of self-adjoint Laplacians

Mathematics Subject Classification ID

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 (2)

Maximal quasi-accretive Laplacians on finite metric graphs ⋮ Hidden symmetries in non-self-adjoint graphs

Cites Work

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• The trace formula for quantum graphs with general self adjoint boundary conditions
• Variational principles for real eigenvalues of self-adjoint operator pencils
• Variational principles for eigenvalues of self-adjoint operator functions
• On the number of negative eigenvalues of the Laplacian on a metric graph
• Kirchhoff's rule for quantum wires
• One-Parameter Semigroups for Linear Evolution Equations
• Quantum graphs: I. Some basic structures
• Quantum Graphs and Their Applications

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