Integral representation of entire functions and differential operators of infinite order

In this article we derive an integral representation in certain spaces of entire functions of exponential type in $\mathbb C^n$. To this end we use the isomorphism, given by the Laplace operator, between these spaces and the corresponding spaces of ultradistributions. Using this integral representation these functions admit a well-defined action of differential operators of infinite order with specific conditions on the characteristic function.