Bases of exponentials, cosines, and sines formed by eigenfunctions of differential operators (Q1778191)

Kadec's famous 1/4-theorem states that if \(\{\lambda_n\}_{n\in \mathbb Z}\) is a real sequence for which \(\sup| n-\lambda_n| <1/4\), then \(\{e^{i\lambda_nt}\}_{n\in \mathbb Z}\) is a Riesz basis for \(L^2(-\pi,\pi)\). The similar result with the complex exponentials replaced by sine-functions or cosine-functions does not hold. By adding assumptions to the Kadec' assumptions, the author provides sufficient conditions for systems of the form \(\{\sin \lambda_n t\}_{n=1}^\infty\) or \(\{1\}\cup \{\cos \lambda_n t\}_{n=1}^\infty\) to form Riesz bases in \(L^2(0,\pi)\).