Electron. J. Differential Equations, Vol. 2019 (2019), No. 03, pp. 1-10.

Eigenfunction expansion for singular Sturm-Liouville problems with transmission conditions

Bilender P. Allahverdiev, Huseyin Tuna

In this work, we show the existence of a spectral function for a singular Sturm-Liouville problem with transmission condition. Also we establish a Parseval equality and expansion formula in eigenfunctions in terms of the spectral function.

Submitted December 11, 2017. Published January 6, 2018.
Math Subject Classifications: 34B24, 34A37, 34L10, 47E05.
Key Words: Sturm-Liouville operator; singular point; transmission condition; spectral function; Parseval equality; eigenfunction expansion.

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Bilender P. Allahverdiev
Department of Mathematics
Suleyman Demirel University
32260 Isparta, Turkey
email: bilenderpasaoglu@sdu.edu.tr
Hüseyin Tuna
Department of Mathematics
Mehmet Akif Ersoy University
15030 Burdur, Turkey
email: hustuna@gmail.com

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