View paper:
pdf dvi ps
View abstract:
pdf gif
links page

Graphical interface
Volume 7
Other volumes
Full text search
of NYJM papers
NYJM home

New York Journal of Mathematics 7 (2001), 117-148.

Multiblock Problems for Almost Periodic Matrix Functions of Several Variables

Leiba Rodman , Ilya M. Spitkovsky, and Hugo J. Woerdeman

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 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/