On recovering Sturm-Liouville operators on graphs

DOI10.1007/S11006-006-0064-0zbMath1123.34006OpenAlexW2371525074MaRDI QIDQ881039

Vjacheslav Anatoljevich Yurko

Publication date: 21 May 2007

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11006-006-0064-0

zbMATH Keywords

inverse spectral problemWeyl functionSturm-Liouville differential operatorKirchhoff conditioncompact graphspectral characteristic

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Inverse problems involving ordinary differential equations (34A55) Boundary value problems on graphs and networks for ordinary differential equations (34B45)

Related Items (12)

Inverse problems for the differential operator on a graph with cycles ⋮ Aharonov-Bohm ring touching a quantum wire: how to model it and to solve the inverse problem ⋮ Self-adjoint restrictions of maximal operator on graph ⋮ Inverse problem solution and spectral data characterization for the matrix Sturm-Liouville operator with singular potential ⋮ Recovering differential pencils on compact graphs ⋮ Schrödinger operators on graphs and geometry I: Essentially bounded potentials ⋮ Uniqueness theorems from partial information of the potential on a graph ⋮ Inverse spectral problems for the Sturm-Liouville operator on a \(d\)-star graph ⋮ On recovering the Sturm-Liouville differential operators on time scales ⋮ An Inverse Spectral Problem for Sturm – Liouville Operators with Singular Potentials on Graphs with a Cycle ⋮ Can one distinguish quantum trees from the boundary? ⋮ Asymptotic Formulae for Weight Numbers of the Sturm – Liouville Boundary Problem on a Star-shaped Graph

Cites Work

• Method of spectral mappings in the inverse problem theory
• The qualitative Sturm-Liouville theory on spatial networks
• Inverse Problem for the Sturm--Liouville Equation on a Simple Graph
• Boundary spectral inverse problem on a class of graphs (trees) by the BC method
• Inverse eigenvalue problems on directed graphs
• On the inverse scattering problem on branching graphs
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