This is not the latest version of this item. The latest version can be found at: https://kops.unikonstanz.de/handle/123456789/32537
Type of Publication:  Journal article 
Publication status:  Submitted 
URI (citable link):  http://nbnresolving.de/urn:nbn:de:bsz:3520316022 
Author:  Goel, Charu; Kuhlmann, Salma; Reznick, Bruce 
Year of publication:  2015 
To Appear in:  Linear Algebra and its Applications ; 2015.  ISSN 00243795.  eISSN 18731856 
ArXivID:  arXiv:1505.08145 
Summary: 
A famous theorem of Hilbert from 1888 states that a positive semidefinite (psd) real form is a sum of squares (sos) of real forms if and only if n=2 or d=1 or (n,2d)=(3,4), where n is the number of variables and 2d the degree of the form. In 1976, Choi and Lam proved the analogue of Hilbert's Theorem for symmetric forms by assuming the existence of psd not sos symmetric nary quartics for n≥5. In this paper we complete their proof by constructing explicit psd not sos symmetric nary quartics for n≥5.

MSC Classification:  11E76, 11E25, 05E05 
Subject (DDC):  510 Mathematics 
Keywords:  Positive Polynomials, Sums of Squares, Symmetric Forms 
Comment on publication:  The previous submission has been improved and split into two papers. The first one being the present version and the second one called "The analogue of Hilbert's 1888 theorem for Even Symmetric Forms" in which we completed our conjecture, namely, an even symmetric nary 2dic psd form is sos if and only if n=2 or d=1 or (n,2d)=(3,8) or (n,2d)=(n,4) for n greater than or equal to 3. 
Link to License:  Terms of use 
Bibliography of Konstanz:  Yes 
GOEL, Charu, Salma KUHLMANN, Bruce REZNICK, 2015. On the ChoiLam analogue of Hilbert's 1888 theorem for Symmetric Forms. In: Linear Algebra and its Applications. ISSN 00243795. eISSN 18731856
@article{Goel2015ChoiL32537.1, title={On the ChoiLam analogue of Hilbert's 1888 theorem for Symmetric Forms}, year={2015}, issn={00243795}, journal={Linear Algebra and its Applications}, author={Goel, Charu and Kuhlmann, Salma and Reznick, Bruce}, note={The previous submission has been improved and split into two papers. The first one being the present version and the second one called "The analogue of Hilbert's 1888 theorem for Even Symmetric Forms" in which we completed our conjecture, namely, an even symmetric nary 2dic psd form is sos if and only if n=2 or d=1 or (n,2d)=(3,8) or (n,2d)=(n,4) for n greater than or equal to 3.} }
Goel_0316022.pdf  72 