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Results tagged with positivity
Search options questions only
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user 66323
10
votes
1
answer
520
views
Conditions for a power of a polynomial to have no negative coefficients
Consider a polynomial in one variable $p(x)$ with $p(0)>0$, and that is not a polynomial in $x^m$ for any $m>1$ (that is, the $gcd$ of the exponents appearing in $p(x)$ is 1). I would like to find nec …
- 407
7
votes
2
answers
754
views
Polynomials such that $|p(z)|\leq p(|z|)$
Let $p(x)=1+p_1x+p_2x^2+\cdots+p_nx^n$ be a polynomial with real coefficients and no positive zeros. Define
$$\mu(x)=\frac{xp'(x)}{p(x)}, \hspace{3ex} \sigma(x)=x \mu'(x).$$
Many years ago, as part of …
- 407