Some Extremal Symmetric Inequalities
Let β_n,d^s := β[x_1,β¦, x_n]_d^π_n be the set of symmetric polynomials of degree d, and A be a compact semialgebraic subset of β_β^n-1. We shall study some PSD cones β(A, β_n,d^s) := {f ββ_n,d^s | f(a) β₯ 0 (β a β A)}. In this article, we study extremal elements of π«(β_+^3, β_3,5^s+), π«(β_+^3, β_3,6^s0), and π«(β^4, β_4,4^s) where π«(β_+^3, β_3,6^s0) := {f βπ«(β_+^3, β_3,6^s) | f(1,β¦,1)=0 }.
READ FULL TEXT