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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A fundamental inequality in the convolution of $ L\sb{2}$ functions on the half line


Author: Saburou Saitoh
Journal: Proc. Amer. Math. Soc. 91 (1984), 285-286
MSC: Primary 30C40; Secondary 26D20
MathSciNet review: 740187
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Abstract: For any positive integer $ q$ and $ {F_j} \in {L_2}(0,\infty )$, we note the inequality for the iterated convolution $ \prod _{j = 1}^{2q} * {F_j}\;$ of $ {F_j}$:

$\displaystyle \int_0^\infty {{{\left\vert {\prod\limits_{j = 1}^{2q} { * {F_j}(... ...s_{j = 1}^{2q} {\int_0^\infty {{{\left\vert {{F_j}(t)} \right\vert}^2}dt.} } } $


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0740187-5
PII: S 0002-9939(1984)0740187-5
Keywords: Convolution, Paley-Wiener theorem, Laplace transform
Article copyright: © Copyright 1984 American Mathematical Society