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Algebra i Analiz, 2007, Volume 19, Issue 4, Pages 146–173 (Mi aa132)  

This article is cited in 9 scientific papers (total in 9 papers)

Research Papers

Operator-valued bergman inner functions as transfer functions

A. Olofsson

Stockholm, Sweden

Abstract: An explicit construction characterizing the operator-valued Bergman inner functions is given for a class of vector-valued standard weighted Bergman spaces in the unit disk. These operator-valued Bergman inner functions act as contractive multipliers from the Hardy space into the associated Bergman space, and they have a natural interpretation as transfer functions for a related class of discrete time linear systems. This points to a new interaction between the fields of invariant subspace theory and mathematical systems theory.

Keywords: Bergman inner function, transfer function, $n$-hypercontraction, wandering subspace, standard weighted Bergman space, discrete time linear system.

Full text: PDF file (248 kB)
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English version:
St. Petersburg Mathematical Journal, 2008, 19:4, 603–623

Bibliographic databases:

MSC: Primary 47A48; Secondary 47A15
Received: 04.09.2006
Language:

Citation: A. Olofsson, “Operator-valued bergman inner functions as transfer functions”, Algebra i Analiz, 19:4 (2007), 146–173; St. Petersburg Math. J., 19:4 (2008), 603–623

Citation in format AMSBIB
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\paper Operator-valued bergman inner functions as transfer functions
\jour Algebra i Analiz
\yr 2007
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\pages 146--173
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\transl
\jour St. Petersburg Math. J.
\yr 2008
\vol 19
\issue 4
\pages 603--623
\crossref{https://doi.org/1090/S1061-0022-08-01013-3}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Olofsson A., “An expansive multiplier property for operator-valued Bergman inner functions”, Math. Nachr., 282:10 (2009), 1451–1460  crossref  mathscinet  zmath  isi
    2. Ball J.A., Bolotnikov V., “Weighted Bergman Spaces: Shift-Invariant Subspaces and Input/State/Output Linear Systems”, Integr. Equ. Oper. Theory, 76:3 (2013), 301–356  crossref  mathscinet  zmath  isi
    3. Olofsson A., Wennman A., “An Operator Inequality for Weighted Bergman Shift Operators”, Rev. Mat. Iberoam., 29:3 (2013), 789–808  crossref  mathscinet  zmath  isi
    4. Olofsson A., “Parts of Adjoint Weighted Shifts”, J. Operat. Theor., 74:2 (2015), 249–280  crossref  mathscinet  zmath  isi
    5. Ball J.A. Bolotnikov V., “on the Expansive Property of Inner Functions in Weighted Hardy Spaces”, Complex Analysis and Dynamical Systems Vi, Pt 2: Complex Analysis, Quasiconformal Mappings, Complex Dynamics, Contemporary Mathematics, 667, ed. Agranovsky M. BenArtzi M. Galloway G. Karp L. Khavinson D. Reich S. Weinstein G. Zalcman L., Amer Mathematical Soc, 2016, 47–61  crossref  zmath  isi
    6. Bhattacharjee M., Eschmeier J., Keshari D.K., Sarkar J., “Dilations, Wandering Subspaces, and Inner Functions”, Linear Alg. Appl., 523 (2017), 263–280  crossref  mathscinet  zmath  isi  scopus
    7. Eschmeier J., “Bergman Inner Functions and M-Hypercontractions”, J. Funct. Anal., 275:1 (2018), 73–102  crossref  mathscinet  zmath  isi
    8. Popescu G., “Invariant Subspaces and Operator Model Theory on Noncommutative Varieties”, Math. Ann., 372:1-2 (2018), 611–650  crossref  mathscinet  zmath  isi  scopus
    9. Popescu G., “Noncommutative Hyperballs, Wandering Subspaces, and Inner Functions”, J. Funct. Anal., 276:11 (2019), 3406–3440  crossref  mathscinet  zmath  isi  scopus
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