A fundamental inequality in the convolution of $L_{2}$ functions on the half line
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- by Saburou Saitoh PDF
- Proc. Amer. Math. Soc. 91 (1984), 285-286 Request permission
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 ${F_j}$: \[ \int _0^\infty {{{\left | {\prod \limits _{j = 1}^{2q} { * {F_j}(t)} } \right |}^2}{t^{1 - 2q}}dt \leqslant \frac {1}{{(2q - 1)!}}\prod \limits _{j = 1}^{2q} {\int _0^\infty {{{\left | {{F_j}(t)} \right |}^2}dt.} } } \]References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 285-286
- MSC: Primary 30C40; Secondary 26D20
- DOI: https://doi.org/10.1090/S0002-9939-1984-0740187-5
- MathSciNet review: 740187