Enclosure of the Zero Set of Polynomials in Several Complex Variables

Authors:
F. G. Boese;W. J. Luther
Affiliations:
Max-Planck-Institut für Extraterrestrische Physik Garching and Gerhard-Mercator-Universität Duisburg. E-mail: gub@mpe.mpg.de;Max-Planck-Institut für Extraterrestrische Physik Garching and Gerhard-Mercator-Universität Duisburg. E-mail: luther@informatik.uni-duisburg.de
Venue:
Multidimensional Systems and Signal Processing
Year:
2001

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Abstract

The zero set of one general multivariate polynomial is enclosed by unions and intersections of simple unbounded sets. Sets in which multivariate real polynomials exhibit constant sign or stay positive are found. Families of stable and unstable polynomials are explicitly given. Stability means here zero-free in the closed unit n-disk or the n-disk complement. The results achieved are discussed and illustrated by examples.