Uniform convergence of the spectral expansions in terms of root functions for a spectral problem

Abstract

In this article, we consider the spectral problem $$\displaylines{ -y''+q(x)y=\lambda y,\quad 0<x<1,\cr y'(0)\sin \beta =y(0)\cos \beta , \quad 0\le \beta <\pi ; \quad y'(1)=(a\lambda +b)y(1) }$$ where $\lambda $ is a spectral parameter, a and b are real constants and a<0, q(x) is a real-valued continuous function on the interval [0,1]. The root function system of this problem can also consist of associated functions. We investigate the uniform convergence of the spectral expansions in terms of root functions.

Keywords

• Differential Operator
• eigenvalues
• root functions
• uniform convergence of spectral expansion