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# Compressed resolvents of selfadjoint contractive exit space extensions and holomorphic operator-valued functions associated with them

### Abstract

Contractive selfadjoint extensions of a Hermitian contraction $B$ in a Hilbert space $\mathfrak H$ with an exit in some larger Hilbert space $\mathfrak H\oplus\mathcal H$ are investigated. This leads to a new geometric approach for characterizing analytic properties of holomorphic operator-valued functions of Krein-Ovcharenko type, a class of functions whose study has been recently initiated by the authors. Compressed resolvents of such exit space extensions are also investigated leading to some new connections to transfer functions of passive discrete-time systems and related classes of holomorphic operator-valued functions.

Key words: Selfadjoint extension, compressed resolvent, transfer function.

### Article Information

 Title Compressed resolvents of selfadjoint contractive exit space extensions and holomorphic operator-valued functions associated with them Source Methods Funct. Anal. Topology, Vol. 21 (2015), no. 3, 199-224 MathSciNet MR3521692 zbMATH 06630268 Milestones Received 01/02/2015; Revised 20/02/2015 Copyright The Author(s) 2015 (CC BY-SA)

### Authors Information

Yu. M. Arlinskiĭ
Department of Mathematical Analysis, East Ukrainian National University; Department of Mathematics, Dragomanov National Pedagogical University, 9 Pirogova Str., Kyiv, 01601, Ukraine

S. Hassi
Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, 65101 Vaasa, Finland

### Citation Example

Yu. M. Arlinskiĭ and S. Hassi, Compressed resolvents of selfadjoint contractive exit space extensions and holomorphic operator-valued functions associated with them, Methods Funct. Anal. Topology 21 (2015), no. 3, 199-224.

### BibTex

@article {MFAT777,
AUTHOR = {Arlinskiĭ, Yu. M. and Hassi, S.},
TITLE = {Compressed resolvents of selfadjoint contractive exit space extensions and holomorphic operator-valued functions associated with them},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {21},
YEAR = {2015},
NUMBER = {3},
PAGES = {199-224},
ISSN = {1029-3531},
MRNUMBER = {MR3521692},
ZBLNUMBER = {06630268},
URL = {http://mfat.imath.kiev.ua/article/?id=777},
}

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