a bounded analytic function on both real and imaginary axis
62568
Does there exists an entire function $f: \mathbb C \to \mathbb C$ which is bounded on real line and imaginary line?
2527
Entire function bounded by a polynomial is a polynomial
112739
The derivative of a holomorphic function on the boundary of the unit circle
111233
Analytic function and the Lagrange interpolating polynomial
106175
A function is analytic if and only if it is holomorphic
116092
Non constant analytic function from $\{z\in\mathbb{C}:z\neq 0\}$ to $\{z\in\mathbb{C}:|z|>1\}.$
138329
Complex Analysis analytic function problem
77644
polynomial converges uniformily to analytic function
5440
Maximum of sum of finite modulus of analytic function.
39583
ii) Show that $u$ is not a real part of the function which analytic on $\mathbb{C} \backslash \lbrace 0 \rbrace$
141863
If the imaginary part of an entire function is never zero, the function is constant
148474
on the boundary of analytic functions
64748
analytic in open unit disk,corresponding to a bounded sequence and a bounded functional sequence
59745
Behavior of holomorphic functions on the boundary of the unit disk
64172
Show that if $f$ is analytic in a domain $D$ and $|f(z)|$ is constant in $D$, then the function $f(z)$ is constant in $D$
35787
An entire function with a bound on its integral is constant
101776
Bounded solution for an equation