Szegő type polynomials and para-orthogonal polynomials
The authors consider Szegő-type polynomials with respect to a linear functional \(\mathcal{M}\) for which the moments \(\mathcal{M}[t^n]=\mu_{-n}\) are all complex, \(\mu_{-n}=\mu_{n}\) and the associated Toeplitz determinants \(D_n\neq 0\) for \(n\geq 0.\) Recurrence relations involving the Szegő-type polynomials and their inverted polynomials are proved. The authors introduce para-orthogonal polynomials and study their basic properties. In the second part of the paper, starting from the existence of polynomials similar to para-orthogonal polynomials, the authors derive sufficient conditions for the existence of Szegő-type polynomials. Finally, the authors give several interesting examples to justify their results.
scientific article; zbMATH DE number 5757935
scientific article