Functions of exponential type and the cardinal series

In this paper, various growth rates and oscillation conditions for entire functions of exponential type ππ are given which ensure validity of the classical cardinal series. Among other applications, a theorem of Plancherel and Polya is extended to show that any function of exponential type ππ which decays to 0 along the real axis is a convergent cardinal series. Examples of functions which show the limitations of this extension are also presented.