Uniform Convergence Of The Spectral Expansions In Terms Of Root Functions For A Spectral Problem

Abstract

In this article, we consider the spectral problem −y 00 + q(x)y = λy, 0 < x < 1, y 0 (0) sin β = y(0) cos β, 0 ≤ β < π; y 0 (1) = (aλ + b)y(1) where λ 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.