Entire majorants via Euler–Maclaurin summation
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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 $f_n(x)=\text {sgn}(x)x^n$, 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.References
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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
- Received by editor(s): January 24, 2003
- Published electronically: February 14, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2216247