Whittaker's cardinal function in retrospect

Authors:
J. McNamee, F. Stenger and E. L. Whitney

Journal:
Math. Comp. **25** (1971), 141-154

MSC:
Primary 41A30; Secondary 65R05

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 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 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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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1971-0301428-0

Keywords:
Cardinal function,
interpolation,
quadrature,
complex

Article copyright:
© Copyright 1971
American Mathematical Society