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Uniform Bounds for Sampling Expansions

✍ Scribed by Xin Min Li

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
221 KB
Volume
93
Category
Article
ISSN
0021-9045

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✦ Synopsis

Let f # B 2 _ , i.e., f # L 2 (R) and its Fourier transform F(s)= R f (t) e &2?ist dt vanishes outside of [&_, _], then the Shannon sampling theorem says that f can be reconstructed by its infinitely many sampling points at [kΓ‚(2_)], k # Z, i.e.,

But, in practice, only finitely many samples are available, so one would like to study the truncation error

The error bounds commonly seen in literature are not uniform. In this paper, the author gives uniform bounds for the truncation error for f # B 2 _ , when its Fourier transform satisfies some smooth conditions.

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The asymptotic behaviour of the Charlier polynomials C (a) n (x) as n Q . is examined. These polynomials satisfy a discrete orthogonality relation and, unlike classical orthogonal polynomials, do not satisfy a second-order linear differential equation with respect to the independent variable x. As s