TY - JOUR

T1 - The analogue of Hilbert's 1888 theorem for even symmetric forms

AU - Goel, Charu

AU - Kuhlmann, Salma

AU - Reznick, Bruce

N1 - Publisher Copyright:
© 2016 Elsevier B.V.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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=2 or d=1 or (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=2 or d=1 or (n,2d)=(n,4)n≥3 or (n,2d)=(3,8).

AB - 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=2 or d=1 or (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=2 or d=1 or (n,2d)=(n,4)n≥3 or (n,2d)=(3,8).

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U2 - 10.1016/j.jpaa.2016.10.003

DO - 10.1016/j.jpaa.2016.10.003

M3 - Article

AN - SCOPUS:85006154106

VL - 221

SP - 1438

EP - 1448

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 6

ER -