Journal of Applied Mathematics

The Modified Parseval Equality of Sturm-Liouville Problems with Transmission Conditions

Mudan Bai, Jiong Sun, and Siqin Yao

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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 λ 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.

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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.

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