Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 71, pp. 1-8.
Title: Riesz bases generated by the spectra of Sturm-Liouville problems
Authors: Tigran Harutyunyan (Yerevan State Univ., Armenia)
Avetik Pahlevanyan (Yerevan State Univ., Armenia)
Anna Srapionyan (Yerevan State Univ., Armenia)
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.
Submitted November 19, 2012. Published March 17, 2013.
Math Subject Classifications: 34B24, 42C15, 34L10.
Key Words: Sturm-Liouville problem; eigenvalues; Riesz bases.