Simultaneous Diophantine approximation: sums of squares and homogeneous polynomials
نویسندگان
چکیده
منابع مشابه
Convexifying Positive Polynomials and Sums of Squares Approximation
We show that if a polynomial f ∈ R[x1, . . . , xn] is nonnegative on a closed basic semialgebraic set X = {x ∈ Rn : g1(x) ≥ 0, . . . , gr(x) ≥ 0}, where g1, . . . , gr ∈ R[x1, . . . , xn], then f can be approximated uniformly on compact sets by polynomials of the form σ0 + φ(g1)g1 + · · ·+ φ(gr)gr, where σ0 ∈ R[x1, . . . , xn] and φ ∈ R[t] are sums of squares of polynomials. In particular, if X...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2019
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa180614-18-9