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arxiv: 1505.04599 · v1 · pith:SDR4Q2KOnew · submitted 2015-05-18 · 🧮 math.FA

Convolvability and regularization of distributions

classification 🧮 math.FA
keywords distributionsconvolvabilitymathcalpropertiesregularizationspacesapplycharacterization
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We apply L.~Schwartz' theory of vector valued distributions in order to simplify, unify and generalize statements about convolvability of distributions, their regularization properties and topological properties of sets of distributions. The proofs rely on propositions on the multiplication of vector-valued distributions and on the characterization of the spaces $\mathcal{O}_{M}(E,F)$ and $\mathcal{O}_{C}'(E,F)$ of multipliers and convolutors for distribution spaces $E$ and $F$.

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