Convergence and summability of cardinal sine series

We consider a class of summability methods for the classical cardinal sine series that are related to the Bernstein-Boas representation of entire functions of exponential type less than pi. We provide conditions that ensure regularity of the methods, prove a Tauberian type theorem, and give an example of a function in the Bernstein class B-pi whose samples do not give rise to a convergent cardinal sine series and are not summable via the methods that are considered here.