Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2013 (2013), Article ID 619358, 11 pages.
The Modified Parseval Equality of Sturm-Liouville Problems with Transmission Conditions
We consider the Sturm-Liouville (S-L) problems with very general transmission conditions on a finite interval. Firstly, we obtain the sufficient and necessary condition for being an eigenvalue of the S-L problems by constructing the fundamental solutions of the problems and prove that the eigenvalues of the S-L problems are bounded below and are countably infinite. Furthermore, the asymptotic formulas of the eigenvalues and eigenfunctions of the S-L problems are obtained. Finally, we derive the eigenfunction expansion for Green's function of the S-L problems with transmission conditions and establish the modified Parseval equality in the associated Hilbert space.
J. Appl. Math., Volume 2013 (2013), Article ID 619358, 11 pages.
First available in Project Euclid: 14 March 2014
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Bai, Mudan; Sun, Jiong; Yao, Siqin. The Modified Parseval Equality of Sturm-Liouville Problems with Transmission Conditions. J. Appl. Math. 2013 (2013), Article ID 619358, 11 pages. doi:10.1155/2013/619358. https://projecteuclid.org/euclid.jam/1394808207