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 $\{\cos ({\lambda }_{n}x){\}}_{n=0}^{\infty }$ or $\{\sin ({\lambda }_{n}x){\}}_{n=0}^{\infty }$ form Riesz bases in $L^2[0,\pi ]$? The answer is almost always positive.

8 pages