Ambarzumian's theorem for a Sturm-Liouville boundary value problem on a star-shaped graph

DOI10.1007/s10688-005-0029-1zbMath1118.34304OpenAlexW1966319498MaRDI QIDQ883618

Vyacheslav N. Pivovarchik

Publication date: 5 June 2007

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10688-005-0029-1

zbMATH Keywords

inverse problemNeumann boundary conditionsleast eigenvalueminimax principlemultiplicity of an eigenvaluenormal eigenvalue

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Inverse problems involving ordinary differential equations (34A55)

Related Items (12)

Schrödinger operators on graphs and geometry. III. General vertex conditions and counterexamples ⋮ Inverse Sturm-Liouville spectral problem on symmetric star-tree ⋮ Ambarzumyan-type theorem for the impulsive Sturm-Liouville operator ⋮ Recovering the shape of a quantum graph ⋮ Spectral determinants and an Ambarzumian type theorem on graphs ⋮ An Ambarzumian-type theorem on graphs with odd cycles ⋮ Inverse Sturm–Liouville problem on equilateral regular tree ⋮ Ambarzumyan-type theorems for the Sturm-Liouville equation on a graph ⋮ Ambarzumyan theorems for Dirac operators ⋮ Schrödinger operators on graphs and geometry. II: Spectral estimates for \(L_1\)-potentials and an Ambartsumian theorem ⋮ Ambarzumyan-type theorems on graphs with loops and double edges ⋮ Asymptotically isospectral quantum graphs and generalised trigonometric polynomials

Cites Work

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• Weakly coupled states on branching graphs
• Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
• Inverse Problem for the Sturm--Liouville Equation on a Simple Graph
• Scattering on graphs and one-dimensional approximations to N-dimensional Schrödinger operators
• On the n -dimensional Ambarzumyan's theorem
• On the Extension of Ambarzumian's Inverse Spectral Theorem to Compact Symmetric Spaces
• Inverse eigenvalue problems on directed graphs

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