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Entire majorants via Euler-Maclaurin summation


Author: Friedrich Littmann
Journal: Trans. Amer. Math. Soc. 358 (2006), 2821-2836
MSC (2000): Primary 42A10; Secondary 42A38
DOI: https://doi.org/10.1090/S0002-9947-06-04121-3
Published electronically: February 14, 2006
MathSciNet review: 2216247
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Abstract: It is the aim of this article to give extremal majorants of type $ 2\pi\delta$ for the class of functions $ f_n(x)=$sgn$ (x)x^n$, 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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Additional Information

Friedrich Littmann
Affiliation: Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105-5075
Email: Friedrich.Littmann@ndsu.edu

DOI: https://doi.org/10.1090/S0002-9947-06-04121-3
Received by editor(s): January 24, 2003
Published electronically: February 14, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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