query: Real part of a holomorphic function is bounded by polynomial then the holomorphic function is a polynomial
positive_passages.docid: 139614
positive_passages.text: Polynomial bounded real part of an entire function
negative_passages.docid: 133099
negative_passages.text: Decomposition of holomorphic function as a sum of entire functions
negative_passages.docid: 115863
negative_passages.text: Every harmonic function is the real part of a holomorphic function
negative_passages.docid: 87723
negative_passages.text: Show a holomorphic function on unit disc with with $|f'(z) - f'(0)| < |f'(0)|$ is injective
negative_passages.docid: 96116
negative_passages.text: Show $P(z) $ is a polynomial of degree $n-1$ interpolating an Analytic function.
negative_passages.docid: 146506
negative_passages.text: If a complex function $f$ is Entire, and there exist $k,R > 0$, $n \in N$ such that $|f(z)| > k|z|^n$ for all $|z| > R$, then f is a polynomial.
negative_passages.docid: 82771
negative_passages.text: Proving that any polynomial $p:\mathbb{R}\rightarrow \mathbb{R}$ is not bounded, but its restriction to any bounded set is bounded
negative_passages.docid: 137045
negative_passages.text: The estimate of real and imaginary part of a holomorphic function
negative_passages.docid: 152347
negative_passages.text: Proof that a certain entire function is a polynomial
negative_passages.docid: 83014
negative_passages.text: Holomorphic function interpolating $e^{-n}$
negative_passages.docid: 69090
negative_passages.text: The family of analytic functions with positive real part is normal
negative_passages.docid: 6722
negative_passages.text: to show $f$ is a polynomial in $z$
negative_passages.docid: 77644
negative_passages.text: polynomial converges uniformily to analytic function
negative_passages.docid: 68071
negative_passages.text: If $f$ is a nonconstant entire function such that $|f(z)|\geq M|z|^n$ for $|z|\geq R$, then $f$ is a polynomial of degree atleast $n$.
negative_passages.docid: 110219
negative_passages.text: Bound on the derivative of a holomorphic function at $0$
negative_passages.docid: 5365
negative_passages.text: Bound on $|f'(0)|$ of a holomorphic funtion in the unit disk
negative_passages.docid: 82367
negative_passages.text: Prove that a holomorphic function with postive real part is constant