Factorization of generalized γ-generating matrices
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The class of γ-generating matrices and its subclasses of regular and singular γ-generating matrices were introduced by D. Z. Arov in , where it was shown that every γ-generating matrix admits an essentially unique regular–singular factorization. The class of generalized γ-generating matrices was introduced in [14, 20]. In the present paper, subclasses of singular and regular generalized –generating matrices are introduced and studied. As the main result, a theorem of existence of the regular–singular factorization for a rational generalized γ-generating matrix is proved.
Keywordsγ-generating matrices J-inner matrix-valued function denominator associated pair generalized Schur class reproducing kernel space Potapov–Ginzburg transform Krein–Langer factorization
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- 1.V. M. Adamjan, D. Z. Arov, and M. G. Krein, “Infinite Hankel matrices and generalized problems of Caratheodory–Fejer and I. Schur problems,” Funkts. Anal. Prilozh., 2, No. 4, 1–17 (1968).Google Scholar
- 8.D. Z. Arov, “γ-generating matrices, j-inner matrix-functions and related extrapolation problems,” J. Soviet Math., 52, 3487–3491 (1990); 52, 3421–3425 (1990).Google Scholar
- 11.T. Ya. Azizov and I. S. Iokhvidov, Foundations of the Theory of Linear Operators in Spaces with an Indefinite Metric [in Russian], Nauka, Moscow, 1986.Google Scholar
- 13.V. A. Derkach adn H. Dym, “On linear fractional transformations associated with generalized J-inner matrix functions,” Integ. Eq. Oper. Th., 65, 1–50 (2009).Google Scholar
- 17.M. G. Krein and H. Langer, “Über die verallgemeinerten Resolventen und die characteristische Function eines isometrischen Operators im Raume Πk,” Colloq. Math. Soc. Janos Bolyai, 5, 353–399 (1972).Google Scholar