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An asymptotically sharp form of Ball's integral inequality


Authors: Ron Kerman, Rastislav Ol’hava and Susanna Spektor
Journal: Proc. Amer. Math. Soc. 143 (2015), 3839-3846
MSC (2010): Primary 33F05; Secondary 42A99
DOI: https://doi.org/10.1090/proc/12505
Published electronically: May 22, 2015
MathSciNet review: 3359575
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Abstract: We solve the open problem of determining the second order term in the asymptotic expansion of the integral in Ball's integral inequality. In fact, we provide a method by which one can compute any term in the expansion. We also indicate how to derive an asymptotically sharp form of a generalized Ball's integral inequality.


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Additional Information

Ron Kerman
Affiliation: Department of Mathematics, Brock University, St. Catharines, Ontario, L2S 3A1, Canada
Email: rkerman@brocku.ca

Rastislav Ol’hava
Affiliation: Department of Mathematics, Charles University, Sokolovska 83, Prague, Czech Republic
Email: olhavara@centrum.sk

Susanna Spektor
Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
Email: spektor@ualberta.ca

DOI: https://doi.org/10.1090/proc/12505
Keywords: Ball's integral inequality, Sinc function, asymptotic expansion, Bessel function
Received by editor(s): July 15, 2013
Received by editor(s) in revised form: March 3, 2014
Published electronically: May 22, 2015
Additional Notes: The research of the second author was supported by grant No. P201-13-14743S of the Grant Agency of the Czech Republic and by the grant SVV-2013-267316.
Communicated by: Walter Van Assche
Article copyright: © Copyright 2015 American Mathematical Society