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Results tagged with positivity
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user 25510
11
votes
Accepted
Conditions for a power of a polynomial to have no negative coefficients
Marcus Michelen, Julian Sahasrabudhe, A characterization of polynomials whose high powers have non-negative coefficients,
https://arxiv.org/abs/1910.06890
- 91.8k
9
votes
Polynomials such that $|p(z)|\leq p(|z|)$
The result proved in the answer of @Terry Tao is actually due to Teichmuller, see, for example
L. Ahlfors, Conformal invariants, section 3-4.
For an interesting related result, see
MR0344465
Boĭčuk, V …
- 91.8k
1
vote
Accepted
Does every locally positive-definite function have a positive-definite extension?
This is true for $d=1$ (M. Krein) but not true for $d>1$ (W. Rudin). For a criterion of extension see
O. Jorgensen, R. Niedzialomski,
Extension of positive definite functions,
J. Math. Anal. Appl. …
- 91.8k
10
votes
Positivity of a one-variable rational function
One can show that all coefficients with sufficiently large index are positive. Indeed, using Maple, the pole of $f$ closest to the origin is:
$a:=0.543689...>0,$
and the residue at this pole is $c:=-0 …
- 91.8k