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> Volume 7, Issue 9
Preprint: Bezout Identities with Inequality Constraints

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wlawton@cz3.nus.edu.sg Guest

Posted: Tue Sep 15, 1998 10:20 am Subject: Preprint: Bezout Identities with Inequality Constraints




#4 Preprint: Bezout Identities with Inequality Constraints
Title: Bezout Identities with Inequality Constraints
Authors: Wayne M. Lawton and Charles A. Micchelli
Abstract:
This paper examines the set $BB(P) = { Q : P cdot Q =
1, , Q in RR^{m} }$ where $P in RR^{m}$ is unimodular
and $RR$ is either the algebra $PP_{R}$ of algebraic
polynomials which are realvalued on the cube $I^{d}$ or the
algebra $LL_{R}$ of Laurent polynomials which are
realvalued on the torus $T^d.$ We sharpen previous results
for the case $m = 2,$ $d = 1$ by showing that if $P$ is
nonnegative, then there exists a positive $Q in BB(P)$
whose length is bounded by a function of the length of $P$ and
the separation between the zeros of $P.$ In the general case
we employ the QuillenSuslin theorem, the Swan theorem, the
Weierstrass approximation theorem and the Michael selection
theorem to prove a result about the existence of solutions to
the B'ezout identity with inequality constraints.
A postscript version of this paper can be obtained via Netscape
from the resume on homepage
http://www.cz3.nus.edu.sg/~wlawton 





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