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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Riemann's function has an exponential bound


Author: Paul R. Beesack
Journal: Proc. Amer. Math. Soc. 88 (1983), 313-316
MSC: Primary 26D15; Secondary 35L99
DOI: https://doi.org/10.1090/S0002-9939-1983-0695265-5
MathSciNet review: 695265
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Abstract: The Riemann function $ \upsilon (t;x)$ of a hyperbolic characteristic initial value problem has been much used in recent years to provide upper bounds for functions which satisfy Gronwall-type integral inequalities. This note gives a direct proof of the fact that $ \upsilon $ satisfies an inequality of the form $ \upsilon (t;x) \leqslant \exp (\int_t^x {b(s)ds}$.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0695265-5
Article copyright: © Copyright 1983 American Mathematical Society