entire function that maps real line to itself is linear
82079
Holomorphic function satisfying $f^{-1}(\Bbb R)=\Bbb R$ is of the form $f(z)=az+b$
3818
Proving two entire functions are constant.
6636
Is there a positive function $f$ on real line such that $f(x)f(y)\le|x-y|, \forall x\in \mathbb Q , \forall y \in \mathbb R \setminus \mathbb Q$?
82371
$f$ is an entire function with Im $f\geq 0$
36379
Suppose that $ f $ is entire and that for each $ z $, either $ |f(z)| \leq 1 $ or $ |f^\prime (z) |\leq 1 $. Prove that $ f $ is a linear polynomial.
68617
Show that an entire function that is real only on the real axis has at most one zero, without the argument principle
144557
Linearly independent functionals
6118
Homeomorphism of the real line-Topology
135772
how to show image of a non constant entire function is dense in $\mathbb{C}$?
97579
showing a function defined from an integral is entire
57504
Why are linear functions linear?
152347
Proof that a certain entire function is a polynomial
90685
The composition of non-linear entire functions with no fixed points has infinitely many fixed points.
107389
Show that the vector space of real functions is not finitely spanned
26687
Show that $f$ maps the unit circle to itself
12349
a construction of a continuous function from a normal space to [0,1]
69845
Construct a real function with is exactly $C^2$ such that its first derivative does not vanish everywhere