A generalization of Borg's inverse theorem for Hill's equations

DOI10.1016/0022-247X(84)90195-1zbMath0557.34021MaRDI QIDQ762329

Harry Hochstadt

Publication date: 1984

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

spectrumHill's equation

Mathematics Subject Classification ID

Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (12)

On the Neumann eigenvalues for second-order Sturm-Liouville difference equations ⋮ Integration of a loaded Korteweg-de Vries equation in a class of periodic functions ⋮ Inverse problem for Hill equation with jump conditions ⋮ On Ambarzumian type theorems for tree domains ⋮ On the modified Korteweg-de-Vries equation with loaded term ⋮ On three spectra problem and Ambarzumian's theorem ⋮ Periodic Jacobi matrices on trees ⋮ Integration of the nonlinear Korteweg-de Vries equation with an additional term ⋮ Cauchy problem for the loaded Korteweg-de Vries equation in the class of periodic functions ⋮ Unnamed Item ⋮ Integration of higher Korteweg-de Vries equation with a self-consistent source in class of periodic functions ⋮ An inverse spectral theorem for a Hill's matrix

Cites Work

• An inverse problem for a differential operator with a mixed spectrum
• Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
• On the determination of a differential equation from its spectral function
• An Inverse Problem for a Hill’s Equation
• Shorter Notes: On a Hill's Equation with Double Eigenvalues
• The inverse problem for periodic potentials
• On the determination of a Hill's equation from its spectrum

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