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           This is an abridged version of a forthcoming paper.
           This work was supported by the 
         % Applied Mathematical Sciences subprogram 
         % of the Office of Energy Research, 
           Office of Scientific Computing,
           U.S. Department of Energy, 
           under Contract W-31-109-Eng-38.}}
\newcommand{\ads}{                          \\[2ex]
        Mathematics and Computer Science Division  \\
        Argonne National Laboratory                 \\
        Argonne, IL 60439-4844 \\
        E-mail: \quad  {\tt kwong@mcs.anl.gov \quad  tang@mcs.anl.gov}}
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\title{$ W $-Matrices, Nonorthogonal Multiresolution Analysis, and Finite Signals of Arbitrary Length}
\date{}\author{Man Kam Kwong and P. T. Peter Tang\ack\add} \maketitle

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\input wm1.tex
\input wm2.tex
\input wm3.tex
\input wm4.tex
\input wm5.tex
\input wm6.tex
\input wm7.tex
\input wmb.tex
\end{document}
