On the spectrum of tridiagonal operators in the context of orthogonal polynomials

The basis for our studies is a large class of orthogonal polynomial sequences \((P_n)_{n\in {{\mathbb {N}}}_0}\) ${(P_n)}_{n\in {\mathbb{N}}_0}$ , which is normalized by \(P_n(x_0)=1\) $P_n(x_0)=1$ for all \(n\in {\mathbb {N}}_0\) $n\in {\mathbb{N}}_0$ where the coefficients in the three-term recurrence relation are bounded. The goal is to check if \(x_0 \in {\mathbb {R}}\) $x_0\in \mathbb{R}$ is in the support of the orthogonalization measure \(\mu \) $\mu$ . For this purpose, we use, among other things, a result of G. H. Hardy concerning Cesàro operators on weighted \(l^2\) $l^2$ -spaces. These investigations generalize ideas from Lasser et al. (Arch Math 100:289–299, 2013).