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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Convolution equations in spaces of distributions with one-sided bounded support


Authors: R. Shambayati and Z. Zielezny
Journal: Trans. Amer. Math. Soc. 289 (1985), 707-713
MSC: Primary 46F10; Secondary 45E10, 46F12
MathSciNet review: 784010
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Abstract: Let $ \mathcal{D}\prime(0,\infty )$ be the space of distributions on $ R$ with support in $ [0,\infty )$ and $ \mathcal{S}\prime(0,\infty )$ its subspace consisting of tempered distributions. We characterize the distributions $ S \in \mathcal{D}\prime(0,\infty )$ for which $ S\, \ast \mathcal{D}\prime(0,\infty ) = \mathcal{D}\prime(0,\infty )$, where $ \ast $ is the convolution. We also characterize the distributions $ S \in \mathcal{S}\prime(0,\infty )$ for which $ S \ast \mathcal{S}\prime(0,\infty ) = \mathcal{S}\prime(0,\infty )$.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0784010-7
Article copyright: © Copyright 1985 American Mathematical Society