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

Abstract

AbstractThe basis for our studies is a large class of orthogonal polynomial sequences $$(P_n)_{n\in {{\mathbb {N}}}_0}$$ ( P n ) n ∈ N 0 , which is normalized by $$P_n(x_0)=1$$ P n ( x 0 ) = 1 for all $$n\in {\mathbb {N}}_0$$ n ∈ 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 ∈ R is in the support of the orthogonalization measure $$\mu $$ μ . 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).