Eigenfunction expansion for singular Sturm-Liouville problems with transmission conditions

Abstract

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.

Keywords

• Sturm-Liouville operator
• singular point
• transmission condition
• spectral function
• Parseval equality
• eigenfunction expansion