Geodesic
The zeros of determinants of matrix-valued polynomials that are orthonormal on a~semi-infinite or finite interval
Sbornik. Mathematics, Tome 209 (2018) no. 12, pp. 1745-1755

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Let the sequence of matrix-valued polynomials $(P_j)_{j=0}^{\infty }$ be orthonormal with respect to a nonnegative matrix-valued measure $\sigma $. Assuming that, for some $\alpha,\beta \in \mathbb{R}$, the support of $\sigma $ is contained in the closed set $[\alpha, +\infty)$, $(-\infty, \beta]$ or $[\alpha,\beta]$, the zeros of the polynomials $(\det P_j)_{j=0}^{\infty }$ are shown to lie in the open set $(\alpha, +\infty)$, $(-\infty, \beta)$ or $(\alpha,\beta)$, respectively.v Bibliography: 10 titles.
Keywords: nonnegative matrix-valued measure, orthogonal matrix-valued polynomials, zeros of determinants of orthogonal matrix-valued polynomials
Mots-clés : matrix moment problem. 
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     author = {Yu. M. Dyukarev},
     title = {The zeros of determinants of matrix-valued polynomials that are orthonormal on a~semi-infinite or finite interval},
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     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_12_a3/}
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Yu. M. Dyukarev. The zeros of determinants of matrix-valued polynomials that are orthonormal on a~semi-infinite or finite interval. Sbornik. Mathematics, Tome 209 (2018) no. 12, pp. 1745-1755. http://geodesic.mathdoc.fr/item/SM_2018_209_12_a3/