Pure States , Nonnegative Polynomials and Sums of Squares

Content Provider	Semantic Scholar
Author	Burgdorf, Sabine Scheiderer, Claus Schweighofer, Markus
Copyright Year	2009
Abstract	In recent years, much work has been devoted to a systematic study of polynomial identities certifying strict or non-strict positivity of a polynomial f on a basic closed set K R. The interest in such identities originates not least from their importance in polynomial optimization. The majority of the important results requires the archimedean condition, which implies that K has to be compact. This paper introduces the technique of pure states into commutative algebra. We show that this technique allows an approach to most of the recent archimedean Stellensätze that is considerably easier and more conceptual than the previous proofs. In particular, we reprove and strengthen some of the most important results from the last years. In addition, we establish several such results which are entirely new. They are the first that allow f to have arbitrary, not necessarily discrete, zeros in K. Mathematics Subject Classification (2010). Primary 06F20, 11E25, 13J30; Secondary 06F25, 13A15, 14P10, 26C99, 46L30, 52A99.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://arxiv.org/pdf/0905.4161.pdf
Alternate Webpage(s)	http://www.ems-ph.org/journals/show_pdf.php?iss=1&issn=0010-2571&rank=4&vol=87
Alternate Webpage(s)	https://www.math.uni-konstanz.de/~schweigh/publications/purestates.pdf
Alternate Webpage(s)	http://www.maths.manchester.ac.uk/raag/preprints/0282.pdf
Alternate Webpage(s)	https://kops.uni-konstanz.de/bitstream/handle/123456789/15615/purestates.pdf?isAllowed=y&sequence=2
Alternate Webpage(s)	http://arxiv.org/pdf/0905.4161v1.pdf
Language	English
Access Restriction	Open
Subject Keyword	Discrete mathematics Mathematical optimization Polynomial ring Quantum state Sense of identity (observable entity) Strict function
Content Type	Text
Resource Type	Article