Abstract
AbstractWe prove a new sampling formula and disprove the existence of a Shannon sampling formula for functions in the Hardy space ℋ︁2(ℝ). 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 © 2009 John Wiley & Sons, Ltd.
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