A uniqueness theorem in the in inverse spectral theory of a certain higher-order ordinary differential equation using Paley-Wiener methods

• Autores: E. Andersson
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 72, Nº 1, 2005, págs. 169-184
• Idioma: inglés
• DOI: 10.1112/s0024610704005770
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• Resumen

  • The paper examines a higher-order ordinary differential equation of the form , where , and where the coefficients , , with , satisfy certain regularity conditions and are chosen so that the matrix is hermitean. It is also assumed that . More precisely, it is proved, using Paley-Wiener methods, that the corresponding spectral measure determines the equation up to conjugation by a function of modulus 1. The paper also discusses under which additional conditions the spectral measure uniquely determines the coefficients , , , as well as and the boundary conditions at 0 and at (if any).