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Entire majorants via Euler-Maclaurin summation

Authors:	Friedrich Littmann

Institution:	Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105-5075

Abstract:	It is the aim of this article to give extremal majorants of type $2\pi\delta$ for the class of functions sgn, where $n\in\mathbb{N}$ . As applications we obtain positive definite extensions to $\mathbb{R}$ of $\pm(it)^{-m}$ defined on $\mathbb{R}\backslash-1,1]$ , where $m\in\mathbb{N}$ , optimal bounds in Hilbert-type inequalities for the class of functions $(it)^{-m}$ , and majorants of type $2\pi$ for functions whose graphs are trapezoids.

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