Products of symmetric forms
โ Scribed by Michael Gilpin
- Publisher
- Elsevier Science
- Year
- 1975
- Tongue
- English
- Weight
- 221 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
It is proved that Z~(a+/3)>~A(a)+A ([3). This inequality is generalised for certain symmetric functions defined by Littlewood. Let O(a +/3) = r~(,~+m t, --~,-,+1,,, kt, k2 ..... ~)1. Then we prove that D(a+/3)~>O(a)+O(/3). Here ~.1,/t2, ~-3 ..... ~ is a partition such that ~., >k,\_ l >-.. >~.2>hl.
Let S e n m denote the set of all real symmetric forms of degree m = 2d. Let PS e n m and S e n m denote the cones of positive semidefinite (psd) and sum of squares (sos) elements of S e n m , respectively. For m = 2 or 4, these cones coincide. For m = 6, they do not, and were analyzed in Even Symm