Exponential type

Summary

An entire function is of exponential type if its modulus grows at most like $e^{\tau \abs{z}}$ for some constant $\tau$. The least such $\tau$ is the type of the function. Fourier and Laplace transforms of functions or measures with bounded support are of exponential type, and the Paley–Wiener theorem gives a converse. They are the natural setting of the Paley–Wiener theorem and of Carlson's theorem.