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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Operator-valued Bergman inner functions as transfer functions


Author: A. Olofsson
Original publication: Algebra i Analiz, tom 19 (2007), nomer 5.
Journal: St. Petersburg Math. J. 19 (2008), 603-623
MSC (2000): Primary 47A48; Secondary 47A15
DOI: https://doi.org/10.1090/S1061-0022-08-01013-3
Published electronically: May 9, 2008
MathSciNet review: 2381937
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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.


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Additional Information

A. Olofsson
Affiliation: Falugatan 22 1tr, SE-113 32 Stockholm, Sweden
Email: ao@math.kth.se

DOI: https://doi.org/10.1090/S1061-0022-08-01013-3
Keywords: Bergman inner function, transfer function, $n$-hypercontraction, wandering subspace, standard weighted Bergman space, discrete time linear system
Received by editor(s): September 4, 2006
Published electronically: May 9, 2008
Additional Notes: Supported by the M.E.N.R.T. (France) and the G. S. Magnuson’s Fund of the Royal Swedish Academy of Sciences
Article copyright: © Copyright 2008 American Mathematical Society