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.
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).
UR - http://www.scopus.com/inward/record.url?scp=85006154106&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85006154106&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2016.10.003
DO - 10.1016/j.jpaa.2016.10.003
M3 - Article
AN - SCOPUS:85006154106
SN - 0022-4049
VL - 221
SP - 1438
EP - 1448
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 6
ER -