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Representation and sampling of Hardy functions

โœ Scribed by Amin Boumenir; Vu Kim Tuan

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
135 KB
Volume
33
Category
Article
ISSN
0170-4214

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โœฆ Synopsis

Abstract

We prove a new sampling formula and disprove the existence of a Shannon sampling formula for functions in the Hardy space โ„‹๏ธ^2^(โ„). As a consequence, a new series representation of the Riemann zeta function in the half plane \documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document}$\Re(s){>}\frac{1}{2}$\end{document} is obtained. We also provide various estimates for the truncations error. Copyright ยฉ 2009 John Wiley & Sons, Ltd.

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