Factorization of generalized γ-generating matrices

被引：0

作者：

Sukhorukova O. ^{[1
]}

机构：

[1] Dragomanov National Pedagogical University, Kiev

来源：

Journal of Mathematical Sciences | 2018年 / 234卷 / 1期

关键词：

associated pair; denominator; generalized Schur class; J-inner matrix-valued function; Krein–Langer factorization; Potapov–Ginzburg transform; reproducing kernel space; γ-generating matrices;

D O I：

10.1007/s10958-018-3983-x

中图分类号：

学科分类号：

摘要：

The class of γ-generating matrices and its subclasses of regular and singular γ-generating matrices were introduced by D. Z. Arov in [8], 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. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

引用

页码：82 / 97

页数：15

共 20 条

[1]

Adamjan V.M., Arov D.Z., Krein M.G., Infinite Hankel matrices and generalized problems of Caratheodory–Fejer and I. Schur problems, Funkts. Anal. Prilozh., 2, 4, pp. 1-17, (1968)

[2]

Adamjan V.M., Nondegenerate unitary couplings of semiunitary operators, Funkts. Anal. Prilozh., 7, 4, pp. 1-16, (1973)

[3]

Alpay D., Dijksma A., Rovnyak J., de Snoo H.S.V., Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces, (1997)

[4]

Alpay D., Dym H., On applications of reproducing kernel spaces to the Schur algorithm and rational J unitary factorization. I. Schur methods in operator theory and signal processing, Oper. Theory Adv. Appl., 18, pp. 89-159, (1986)

[5]

Aronszajn N., Theory of reproducing kernels, Trans. Amer. Math. Soc., 68, pp. 337-404, (1950)

[6]

Arov D.Z., Realization of matrix-valued functions according to Darlington, Izv. Akad. Nauk SSSR. Ser. Mat., 37, pp. 1299-1331, (1973)

[7]

Arov D.Z., Regular and singular J-inner matrix functions and corresponding extrapolation problems, Funct. Anal. Appl., 22, 1, pp. 46-48, (1988)

[8]

Arov D.Z., γ-generating matrices, j-inner matrix-functions and related extrapolation problems, J. Soviet Math, 52, pp. 3487-3491, (1990)

[9]

Arov D.Z., Dym H., J-inner matrix function, interpolation and inverse problems for canonical system, I: Foundation, integral equations, Operator Theory, 28, pp. 1-16, (1997)

[10]

Arov D.Z., Dym H., J-Contractive Matrix-Valued Functions and Related Topics, Cambridge Univ, (2008)

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