Cardinal Sine Series: Convergence and Uniqueness

Many aspects of the cardinal sine series, particularly those associated with the mathematical theory of sampling in signal processing, are very well known due to its role in the classical sampling theorems. The objective of this article is to highlight several extensions of these classical theorems and to provide corresponding examples. Among the matter presented here are (i) necessary and sufficient conditions for convergence of the series and (ii) several new classes of entire functions that can be represented via such series. Some of these classes contain members that may be unbounded on the real axis.