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Nuclear Hankel matrices and orthogonal trigonometric polynomials. (English) Zbl 0849.47012

Marcantognini, S. A. M. (ed.) et al., Harmonic analysis and operator theory. A conference in honor of Mischa Cotlar, January 3-8, 1994, Caracas, Venezuela. Proceedings. Providence, RI: American Mathematical Society. Contemp. Math. 189, 1-15 (1995).
Summary: This article is a study of the generalized Schur problem (GSP) in the case when the corresponding infinite Hankel matrix generates a trace class operator. A multiplicative representation in terms of Schur parameters is proposed for the matrix of the linear fractional transformation in the known formula [the first author, D. Z. Arov and M. G. Krejn, Funct. Anal. Appl. 2 (1968), 269-281 (1969; Zbl 0179.46701) and Math. USSR, Sb. 15 (1971), 31-73 (1972; Zbl 0248.47019)] furnishing all solutions of the GSP. In connection with this representation a recurrent system defining Szegö orthogonal trigonometric polynomials with respect to the absolutely continuous measure on the unit circle is investigated.
For the entire collection see [Zbl 0826.00021].

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47A57 Linear operator methods in interpolation, moment and extension problems
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