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 (Pₙ)_n∈ N₀ ( P n ) n ∈ N 0 , which is normalized by Pₙ(x₀)=1 P n ( x 0 ) = 1 for all n∈ N₀ n ∈ N 0 where the coefficients in the three-term recurrence relation are bounded. The goal is to check if x₀ ∈ R x 0 ∈ R is in the support of the orthogonalization measure μ μ . For this purpose, we use, among other things, a result of G. H. Hardy concerning Cesàro operators on weighted l² l 2 -spaces. These investigations generalize ideas from Lasser et al. (Arch Math 100:289–299, 2013).