The analogue of Hilbert's 1888 theorem for even symmetric forms

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• 作者：Charu Goel^a ; ^{charu.goel@uni-konstanz.de} ; Salma Kuhlmann^a ; ^{salma.kuhlmann@uni-konstanz.de} ; Bruce Reznick^b ; ^{reznick@math.uiuc.edu}
• 关键词：11E76 ; 11E25 ; 05E05 ; 14P10
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：221
• 期：6
• 页码：1438-1448
• 全文大小：332 K
• 卷排序：221

文摘

Hilbert proved in 1888 that a positive semidefinite (psd) real form is a sum of squares (sos) of real forms if and only if n=2n=2 or d=1d=1 or (n,2d)=(3,4)(n,2d)=(3,4), where n is the number of variables and 2d the degree of the form. We study the analogue for even symmetric forms. We establish that an even symmetric n-ary 2d  -ic psd form is sos if and only if n=2n=2 or d=1d=1 or (n,2d)=(n,4)n≥3(n,2d)=(n,4)n≥3 or (n,2d)=(3,8)(n,2d)=(3,8).