Abstract
The results of M.G. Krein regarding polynomials that are orthogonal on the unit circle with respect to a sign alternating weight function, are generalized to the case of matrix polynomials. These results are concerned with the distribution of the zeroes of the orthogonal polynomials and with the inverse problem of reconstructing the weight function from a given polynomial.
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Gohberg, I., Lerer, L. (1988). Matrix Generalizations of M. G. Krein Theorems on Orthogonal Polynomials. In: Gohberg, I. (eds) Orthogonal Matrix-valued Polynomials and Applications. Operator Theory: Advances and Applications, vol 34. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5472-6_6
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DOI: https://doi.org/10.1007/978-3-0348-5472-6_6
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