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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
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