Article contents
A generalisation of the inverse spectral theorem of Levitan and Gasymov
Published online by Cambridge University Press: 14 November 2011
Synopsis
In the Inverse Spectral Theorem in the form given by Levitan and Gasymov, necessary and sufficient conditions are given for a non-decreasing function, p(ℷ), to be the spectral function of a Sturm–Liouville problem. In these conditions, p(ℷ) is compared with the spectral function for the particular Strum–Liouville problem
If the method of Levitan and Gasymov's proof is slightly adapted, the necessary and sufficient conditions can be stated in a more general form in which p(ℷ) is compared with the spectral function for any problem of the form
where hO is real and qo(x) locally integrable.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 3-4 , 1979 , pp. 185 - 196
- Copyright
- Copyright © Royal Society of Edinburgh 1979
References
- 8
- Cited by