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3.—Uniqueness of Sturm-Liouville Coefficients*
Published online by Cambridge University Press: 14 February 2012
Synopsis
An analogue of the Riemannian theory of uniqueness of Fourier coefficients is developed for Sturm Liouville series, using asymptotic formulae for the eigenfunctions and other quantities. This theory generalises earlier work by Haar in that the coefficient function in the differential equation is only assumed to be integrable.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 73 , 1975 , pp. 65 - 75
- Copyright
- Copyright © Royal Society of Edinburgh 1975
References
1Haar, A., Zur Theorie der orthogonalen Funktionen-systeme (zweite Milleilung). Math. Ann., 71, 38–53, 1911.Google Scholar
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4Wray, S. D., Sturm-Liouville and singular theory for second-order differential equations (Ph.D. Thesis). Adelaide: Flinders Univ., 1973.Google Scholar
5Zygmund, A., Sur la theorie riemannienne de certains systemes orthogonaux, I. Studia Math., 2, 97–170, 1930.CrossRefGoogle Scholar