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# Factorization formulas for some classes of generalized $J$-inner matrix valued functions

### Abstract

The class $\mathcal{U}_\kappa(j_{pq})$ of generalized $j_{pq}$-inner matrix valued functions (mvf's) %and its subclass $\mathcal{U}^r_\kappa(j_{pq})$ was introduced in [2]. For a mvf $W$ from a subclass $\mathcal{U}^r_\kappa(j_{pq})$ of $\mathcal{U}_\kappa(j_{pq})$ the notion of the right associated pair was introduced in [13] and some factorization formulas were found. In the present paper we introduce a dual subclass $\mathcal{U}^\ell_\kappa(j_{pq})$ and for every mvf $W\in \mathcal{U}^\ell_\kappa(j_{pq})$ a left associated pair $\{\beta_1,\beta_2\}$ is defined and factorization formulas for $W$ in terms of $\beta_1,\beta_2$ are found. The notion of a singular generalized $j_{pq}$-inner mvf $W$ is introduced and a characterization of singularity of $W$ is given in terms of associated pair.

Key words: J-inner matrix valued function, generalized Schur class, Kre˘ın-Langer factorization, Potapov-Ginzburg transform, reproducing kernel space, associated pair.

### Article Information

 Title Factorization formulas for some classes of generalized $J$-inner matrix valued functions Source Methods Funct. Anal. Topology, Vol. 20 (2014), no. 4, 365-378 MathSciNet MR3309673 zbMATH 1324.47032 Milestones Received 24/12/2013; Revised 23/06/2014 Copyright The Author(s) 2014 (CC BY-SA)

### Authors Information

Olena Sukhorukova
Department of Mathematics, Donetsk National University, Donetsk, Ukraine

### Citation Example

Olena Sukhorukova, Factorization formulas for some classes of generalized $J$-inner matrix valued functions, Methods Funct. Anal. Topology 20 (2014), no. 4, 365-378.

### BibTex

@article {MFAT728,
AUTHOR = {Sukhorukova, Olena},
TITLE = {Factorization formulas for some classes of generalized $J$-inner matrix valued functions},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {20},
YEAR = {2014},
NUMBER = {4},
PAGES = {365-378},
ISSN = {1029-3531},
MRNUMBER = {MR3309673},
ZBLNUMBER = {1324.47032},
URL = {http://mfat.imath.kiev.ua/article/?id=728},
}