There is an entire function $f$, that is bounded by polynomial $p(z)$ with degree $n$, meaning that
$|f(z)|≤|p(z)|$ for every $z\in\mathbb C$.
Show that $f$ is a polynomial of degree at most $n$ (less or equal to $n$).
Asked
Active
Viewed 78 times
0
-
What have you tried? – Keen-ameteur Jan 18 '20 at 14:20
-
I tried to suppose "wrong" that f is in a degree n+1. – Kwigy Jan 18 '20 at 14:22
-
meaning f=(z-z0)(z-z1)....(z-zn)(z-z(n+1)) – Kwigy Jan 18 '20 at 14:23
-
And g=(z-z0)(z-z1)....(z-zn). But we now that f is smaller than g. And than I got stuck – Kwigy Jan 18 '20 at 14:23