- #1

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## Homework Statement

Find all entire functions [tex]f[/tex] such that

[tex] |f(z)|\leq e^{\textrm{Re}(z)}\quad\forall z\in\mathbb{C}[/tex]

## Homework Equations

[tex]\textrm{Re}(u+iv)=u[/tex]

## The Attempt at a Solution

I tried using Nachbin's theorem for functions of exponential type. I also tried using the Cauchy integral formula to see if I could gain more information about [tex]f[/tex] but I could not solve the problem.