# Relation between entire function of exponential type and exponential polynomials

Is it true in general that the theory of entire function of exponential type and and that of exponential polynomials (with purely imaginary exponents) are analogous ?

Can one derive results about entire function of exponential type by using results about exponential polynomials ?

For example I am wondering if it is possible to derive sampling theorems about band-limited functions by studying properties of exponential polynomials ?

What about the distribution of zeros ?

Exponential polynomials are very special among the entire functions of exponential type. Their zeros accumulate to finitely many directions: there are finitely many numbers $\{\theta_1,\ldots,\theta_n\}$ such that the arguments of zeros accumulate only to those $\theta_j$. General entire functions of exponential type can have arguments of zeros arbitrarily distributed, for example, uniformly.
Further, $\log M(r)$, where $M(r)=\max_{|z|\leq r}|f(z)|$ for exponential polynomials is like $(c+o(1))r$, while for general entire functions of exponential type, the limit $(\log M(r))/r$ might not exist.