One-parameter semigroups in the convolution algebra of rapidly decreasing distributions

Colloquium Mathematicae, Tome 126 (2012), p. 49-68 / Harvested from The Polish Digital Mathematics Library

Résumé

The paper is devoted to infinitely differentiable one-parameter convolution semigroups in the convolution algebra $_{C}^{'} (ℝ ⁿ; M_{m \times m})$ of matrix valued rapidly decreasing distributions on ℝⁿ. It is proved that $G \in_{C}^{'} (ℝ ⁿ; M_{m \times m})$ is the generating distribution of an i.d.c.s. if and only if the operator $\partial_{t} \otimes_{m \times m} - G *$ on $ℝ^{1 + n}$ satisfies the Petrovskiĭ condition for forward evolution. Some consequences are discussed.

Publié le : 2012-01-01

Zbl 1272.46036

EUDML-ID : urn:eudml:doc:283529

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     volume = {126},
     year = {2012},
     pages = {49-68},
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 (éd.). One-parameter semigroups in the convolution algebra of rapidly decreasing distributions. Colloquium Mathematicae, Tome 126 (2012) pp. 49-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-1-6/