منابع مشابه
Discriminants and nonnegative polynomials
For a semialgebraic set K in R, let Pd(K) = {f ∈ R[x]≤d : f(u) ≥ 0 ∀u ∈ K} be the cone of polynomials in x ∈ R of degrees at most d that are nonnegative on K. This paper studies the geometry of its boundary ∂Pd(K). When K = R n and d is even, we show that its boundary ∂Pd(K) lies on the irreducible hypersurface defined by the discriminant ∆(f) of f . When K = {x ∈ R : g1(x) = · · · = gm(x) = 0}...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1970
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1970-0287244-8