Ambarzumyan-type theorems for the Sturm-Liouville equation on a graph

DOI10.1216/RMJ-2009-39-4-1353zbMath1177.34013MaRDI QIDQ2270592

Zhen-you Huang, Chuan-Fu Yang, Xiao-Ping Yang

Publication date: 28 July 2009

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Sturm-Liouville operatorsinverse spectral problemstar-type graph

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) General theory of ordinary differential operators (47E05) Inverse problems involving ordinary differential equations (34A55) Nonlocal and multipoint boundary value problems for ordinary differential equations (34B10)

Related Items (8)

Inverse problem for differential pencils on a hedgehog graph ⋮ Inverse problems for the differential operator on a graph with cycles ⋮ Inverse problems for differential pencils on A-graphs ⋮ Recovering the shape of a quantum 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

• Ambarzumian's theorem for a Sturm-Liouville boundary value problem on a star-shaped graph
• Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
• Inverse Problem for the Sturm--Liouville Equation on a Simple Graph
• On the n -dimensional Ambarzumyan's theorem
• On an extension of the theorem of V. A. Ambarzumyan
• Inverse spectral problems for Sturm–Liouville operators on graphs
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