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Leiba Rodman, Ilya M. Spitkovsky, and Hugo J. Woerdeman
Multiblock Problems for Almost Periodic Matrix Functions of Several Variables
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| Published: |
September 20, 2001 |
| Keywords: |
Positive multiblock extensions, contractive multiblock extensions, band method, almost periodic matrix functions, Besikovitch spaces, Toeplitz operators, Hankel operators, model matching |
| Subject: |
42A75, 15A54, 47A56, 47A57, 42A82, 47B35, 93B28 |
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Abstract
In this paper we solve positive and contractive multiblock problems in the
Wiener algebra of almost periodic functions of several variables. We thus
generalize the classical four block problem that appears in
robust control in many ways. The necessary and sufficient conditions are in
terms of
appropriate Toeplitz (positive case) and Hankel operators (contractive case) on
Besikovitch space. In addition, a model matching interpretation is given,
and some more general
patterns are treated as
well.
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| Acknowledgements
The research of all authors is partially supported by NSF Grant DMS 9988579. HJW is also partially supported by a Research Grant from the College of William and Mary.
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| Author information
Leiba Rodman:
Department of Mathematics, P. O. Box 8795, The College of William and Mary, Williamsburg VA 23187-8795
lxrodm@math.wm.edu
http://www.math.wm.edu/~lxrodm/
Ilya M. Spitkovsky:
Department of Mathematics, P. O. Box 8795, The College of William and Mary, Williamsburg VA 23187-8795
ilya@math.wm.edu
http://www.math.wm.edu/~ilya/
Hugo J. Woerdeman:
Department of Mathematics, P. O. Box 8795, The College of William and Mary, Williamsburg VA 23187-8795
hugo@math.wm.edu
http://www.math.wm.edu/~hugo/
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