Whittaker's Cardinal Function in Retrospect

J. McNamee, F. Stenger, E. L. Whitney
1971 Mathematics of Computation  
This paper exposes properties of the Whittaker cardinal function and illustrates the use of this function as a mathematical tool. The cardinal function is derived using the Paley-Wiener theorem. The cardinal function and the central-difference expansions are linked through their similarities. A bound is obtained on the difference between the cardinal function and the function which it interpolates. Several cardinal functions of a number of special functions are examined. It is shown how the
more » ... s shown how the cardinal function provides a link between Fourier series and Fourier transforms, and how the cardinal function may be used to solve integral equations.
doi:10.2307/2005140 fatcat:smi3yhvhebfb3ecf72cemlljk4