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Spectral sets of periodic matrices related to the strong moment problem. (English) Zbl 1288.30030
Summary: The main result of this work is a parametric description of the spectral surfaces of a class of periodic 5-diagonal matrices, related to the strong moment problem. This class is a self-adjoint twin of the class of CMV matrices. Jointly they form the simplest possible classes of 5-diagonal matrices.

MSC:
30E05 Moment problems and interpolation problems in the complex plane
30F99 Riemann surfaces
47B39 Linear difference operators
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
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[1] N. Akhiezer and B. Levin, Generalization of S. N. Bernstein’s inequality for derivatives of entire functions. In Issledovanija po sovremennym problemam teorii funkcii kom- pleksnogo peremennogo. Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1960, 111-165. In Russian.
[2] A. I. Aptekarev, Asymptotic properties of polynomials orthogonal on a system of contours, and periodic motions of Toda chains. Mat. Sb. (N.S.) 125 (1984), 231-258. In Russian. · Zbl 0608.42016 · doi:10.1070/SM1986v053n01ABEH002918 · eudml:71614
[3] A. Bogatyrev, A combinatorial description of a moduli space of curves and of ex- tremal polynomials. Mat. Sb. 194 (2003), 27-48. English Transl. Sb. Math. 194 (2003), 1451-1473. · Zbl 1097.14021 · doi:10.1070/SM2003v194n10ABEH000772
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