On five-diagonal Toeplitz matrices and orthogonal polynomials on the unit circle
This paper deals with modifications of the Lebesgue moment functional on the unit circle by trigonometric polynomials of degree 2. The associated Toeplitz matrix is five-diagonal. The authors study the quasi-definiteness and the positive-definiteness of the corresponding moment functional. Further, they use the factorization of a five-diagonal matrix as a product of two tridiagonal matrices [see \textit{R. B. Marr} and \textit{G. H. Vineyard}, SIAM J. Matrix Anal. Appl. 9, No. 4, 579-586 (1988; Zbl 0661.15006)]\ to study the existence of the orthogonal polynomials.
scientific article; zbMATH DE number 784685
scientific article