Whittaker’s cardinal function in retrospect
Authors:
J. McNamee, F. Stenger and E. L. Whitney
Journal:
Math. Comp. 25 (1971), 141154
MSC:
Primary 41A30; Secondary 65R05
DOI:
https://doi.org/10.1090/S00255718197103014280
MathSciNet review:
0301428
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Abstract  References  Similar Articles  Additional Information
Abstract: 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 PaleyWiener theorem. The cardinal function and the centraldifference 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 cardinal function provides a link between Fourier series and Fourier transforms, and how the cardinal function may be used to solve integral equations.

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Keywords:
Cardinal function,
interpolation,
quadrature,
complex
Article copyright:
© Copyright 1971
American Mathematical Society