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Results tagged with positivity
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user 4312
17
votes
Polynomials that preserve nonnegativity
Such a polynomial may be represented as $q^2 +xr^2 $ (proof: this is true for all irreducible divisors which have degree 1 or 2, and the set of polynomials of this kind is a multiplicative monoid by E …
- 109k
6
votes
Accepted
Polynomials $p$ such that $p$ and $p'$ preserve nonnegative numbers
The equivalent condition is $p(0)\geqslant 0$, $p'(x) \geqslant 0$ for $x\geqslant 0$.Thus this class reduces to $\mathscr {P} $ by taking antiderivative.
The inequality $|p(z)|\leqslant p(|z|)$ fa …
- 109k