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