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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

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.

Acknowledgments:
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.
Author information:
Leiba Rodman :
Department of Mathematics, P. O. Box 8795, The College of William and Mary, Williamsburg VA 231878795
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 231878795
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 231878795
hugo@math.wm.edu
http://www.math.wm.edu/~hugo/
 