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   -> Volume 7, Issue 9


Preprint: Bezout Identities with Inequality Constraints
 
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wlawton@cz3.nus.edu.sg
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PostPosted: Tue Sep 15, 1998 10:20 am    
Subject: Preprint: Bezout Identities with Inequality Constraints
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#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 real--valued on the cube $I^{d}$ or the
algebra $LL_{R}$ of Laurent polynomials which are
real--valued on the torus $T^d.$ We sharpen previous results
for the case $m = 2,$ $d = 1$ by showing that if $P$ is
non-negative, 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 Quillen-Suslin 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

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