Electron. J. Diff. Equ., Vol. 2013 (2013), No. 71, pp. 1-8.

Riesz bases generated by the spectra of Sturm-Liouville problems

Tigran Harutyunyan, Avetik Pahlevanyan, Anna Srapionyan

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.

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Tigran Harutyunyan
Faculty of Mathematics and Mechanics, Yerevan State University
1 Alex Manoogian, 0025, Yerevan, Armenia
email: hartigr@yahoo.co.uk
Avetik Pahlevanyan
Faculty of Mathematics and Mechanics, Yerevan State University
1 Alex Manoogian, 0025, Yerevan, Armenia
email: avetikpahlevanyan@gmail.com
Anna Srapionyan
Faculty of Mathematics and Mechanics, Yerevan State University
1 Alex Manoogian, 0025, Yerevan, Armenia
email: srapionyan.anna@gmail.com

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