A study on the uniform convergence of spectral expansions for continuous functions on a Sturm-Liouville problem

Abstract

The paper is about investigating the uniform convergence conditions of spectral expansions of continuous functions in terms of root functions of a spectral problem with the same eigenparameter in the second-order differential equation and depending on quadratically in one of the boundary conditions on a closed interval.

Sturm-Liouville problems with a boundary condition depending affinely or quadratically on an eigenparameter

“…The following theorem was proved in [12] and mentioned in [16]. Again, we skip the cases where no necessary and sufficient conditions appear.…”

“…First example of a double eigenvalue. The following example from [12] was also discussed in [16][17][18]. Consider the spectral problem…”