query: Additional question on Entire function bounded by a polynomial is a polynomial
positive_passages.docid: 23585
positive_passages.text: Show that a holomorphic function satisfying $|f(z)|\leq c|z|^n$ must be $f(z)=a\cdot z^n$ for some a.
negative_passages.docid: 30330
negative_passages.text: How can I prove that this function is bounded using the given 2 hints?
negative_passages.docid: 98399
negative_passages.text: Suppose $f$ and $g$ are entire functions, and $|f(z)| \leq |g(z)|$ for all $z \in \mathbb{C}$, Prove that $f(z)=cg(z)$.
negative_passages.docid: 7755
negative_passages.text: Question on entire function
negative_passages.docid: 29114
negative_passages.text: If $f \in L^{p_1}(E) $ is bounded then $f\in L^{p_2}$ for any $p_2>p_1$
negative_passages.docid: 35787
negative_passages.text: An entire function with a bound on its integral is constant
negative_passages.docid: 56047
negative_passages.text: Radius of convergence of entire function
negative_passages.docid: 86473
negative_passages.text: Find all entire functions such that $|f(z)|\leq |\sin(z)|$ for all $z\in\mathbb C$.
negative_passages.docid: 148486
negative_passages.text: Suppose $f$ is entire and $|f(z)| \leq A + B |z|^{3/2}$. Show that $f$ is a linear polynomial.
negative_passages.docid: 54212
negative_passages.text: Another polynomial equation
negative_passages.docid: 103932
negative_passages.text: How can I prove that a polynomial with degree $n$ is continuous everywhere in $\mathbb{R}$ using definitions?
negative_passages.docid: 15914
negative_passages.text: Prove that any polynomial function is continuous
negative_passages.docid: 33099
negative_passages.text: If $f$ is an entire function where every power series expansion has at least one 0 term, show it is a polynomial
negative_passages.docid: 155575
negative_passages.text: Proving a polynomial $f(x)$ composite for infinitely many $x$
negative_passages.docid: 141078
negative_passages.text: Domain over which a polynomial is strictly positive
negative_passages.docid: 62568
negative_passages.text: Does there exists an entire function $f: \mathbb C \to \mathbb C$ which is bounded on real line and imaginary line?
negative_passages.docid: 4065
negative_passages.text: What are the entire functions $f$ such that $|f'(z)| \leq |f(z)| \ ? $