query: Holomorphic function with constant absolute value
positive_passages.docid: 25520
positive_passages.text: Why: A holomorphic function with constant magnitude must be constant.
negative_passages.docid: 48222
negative_passages.text: Composition of a harmonic function with a holomorphic function is still harmonic
negative_passages.docid: 32789
negative_passages.text: Show bounded harmonic function on $\mathbb{C}$ is constant.
negative_passages.docid: 84374
negative_passages.text: Rational function with absolute value $1$ on unit circle
negative_passages.docid: 136793
negative_passages.text: Does there exist a holomorphic function $\varphi(z)$ such that $\varphi^2(z) = \psi(z)$
negative_passages.docid: 18611
negative_passages.text: An analytic function with a simple pole
negative_passages.docid: 73547
negative_passages.text: Prove that is $\bar{f}g$ is analytic then $f$ is constant or...?
negative_passages.docid: 120533
negative_passages.text: A harmonic function with sublinear growth at infinity is constant
negative_passages.docid: 54196
negative_passages.text: When is a function satisfying the Cauchy-Riemann equations holomorphic?
negative_passages.docid: 109943
negative_passages.text: Estimates of the value of a holomorphic function and its derivative
negative_passages.docid: 13728
negative_passages.text: can $f$ be holomorphic?
negative_passages.docid: 106175
negative_passages.text: A function is analytic if and only if it is holomorphic
negative_passages.docid: 15378
negative_passages.text: Why a holomorphic function satisfying these conditions has to be linear?
negative_passages.docid: 93400
negative_passages.text: Prove that an analytic function with a constant imaginary part is constant itself
negative_passages.docid: 26388
negative_passages.text: proof that function is constant
negative_passages.docid: 82367
negative_passages.text: Prove that a holomorphic function with postive real part is constant
negative_passages.docid: 115863
negative_passages.text: Every harmonic function is the real part of a holomorphic function