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Algebra i Analiz, 2007, Volume 19, Issue 4, Pages 146–173 (Mi aa132)  
This article is cited in 12 scientific papers (total in 12 papers)

Research Papers

Operator-valued bergman inner functions as transfer functions

A. Olofsson

Stockholm, Sweden
Full-text PDF (248 kB) Citations (12)
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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.
Received: 04.09.2006
English version:
St. Petersburg Mathematical Journal, 2008, Volume 19, Issue 4, Pages 603–623
DOI: https://doi.org/1090/S1061-0022-08-01013-3
Bibliographic databases:
Document Type: Article
MSC: Primary 47A48; Secondary 47A15
Language: English
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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\transl
\jour St. Petersburg Math. J.
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\vol 19
\issue 4
\pages 603--623
\crossref{https://doi.org/1090/S1061-0022-08-01013-3}
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Linking options:
  • https://www.mathnet.ru/eng/aa132
  • https://www.mathnet.ru/eng/aa/v19/i4/p146
    • This publication is cited in the following 12 articles:
    1. Abadias L. Bello G. Yakubovich D., “Operator Inequalities, Functional Models and Ergodicity”, J. Math. Anal. Appl., 498:2 (2021), 124984  crossref  mathscinet  isi
    2. Le T., “Inner Functions in Weighted Hardy Spaces”, Anal. Math. Phys., 10:2 (2020), 25  crossref  mathscinet  isi
    3. Hu J., Wang W., “Wandering Subspaces and Inner Operators”, J. Math. Anal. Appl., 491:1 (2020), 124241  crossref  mathscinet  isi  scopus
    4. Popescu G., “Noncommutative Hyperballs, Wandering Subspaces, and Inner Functions”, J. Funct. Anal., 276:11 (2019), 3406–3440  crossref  mathscinet  zmath  isi  scopus
    5. Eschmeier J., “Bergman Inner Functions and M-Hypercontractions”, J. Funct. Anal., 275:1 (2018), 73–102  crossref  mathscinet  zmath  isi
    6. Popescu G., “Invariant Subspaces and Operator Model Theory on Noncommutative Varieties”, Math. Ann., 372:1-2 (2018), 611–650  crossref  mathscinet  zmath  isi  scopus
    7. 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
    8. 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
    9. Olofsson A., “Parts of Adjoint Weighted Shifts”, J. Operat. Theor., 74:2 (2015), 249–280  crossref  mathscinet  zmath  isi
    10. 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
    11. Olofsson A., Wennman A., “An Operator Inequality for Weighted Bergman Shift Operators”, Rev. Mat. Iberoam., 29:3 (2013), 789–808  crossref  mathscinet  zmath  isi  scopus
    12. Olofsson A., “An expansive multiplier property for operator-valued Bergman inner functions”, Math. Nachr., 282:10 (2009), 1451–1460  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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