Riesz bases generated by the spectra of Sturm-Liouville problems

Abstract

Let ${lambda _n^2} _{n = 0}^infty$ be the spectra of a Sturm-Liouville problem on $[0,pi ]$. We investigate the question: Do the systems ${ cos(lambda_nx)} _{n = 0}^infty$ or ${ sin(lambda_n x)} _{n = 0}^infty$ form Riesz bases in ${L^2}[0,pi ]$? The answer is almost always positive.

Keywords

• Sturm-Liouville problem
• eigenvalues
• Riesz bases