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Szego's theorem on Parreau-Widom sets
Jacob S. Christiansen
In this paper, we generalize Szego's theorem for orthogonal polynomials on the real line to infinite gap sets of Parreau-Widom type. This notion includes Cantor sets of positive me…
A question by Chihara about shell polynomials and indeterminate moment problems
Christian Berg, Jacob S. Christiansen
The generalized Stieltjes--Wigert polynomials depending on parameters 0\le p<1 and 0<q<1 are discussed. By removing the mass at zero of the N-extremal solution concentrated in the…
Self-adjoint difference operators and symmetric Al-Salam--Chihara polynomials
Jacob S. Christiansen, Erik Koelink
The symmetric Al-Salam--Chihara polynomials for are associated with an indeterminate moment problem. There is a self-adjoint second order difference operator on …
Self-adjoint difference operators and classical solutions to the Stieltjes--Wigert moment problem
Jacob S. Christiansen, Erik Koelink
The Stieltjes-Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We cons…