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

(2012)

Colloquium Mathematicae

The paper is devoted to infinitely differentiable one-parameter convolution semigroups in the convolution algebra C ' ( ; M m × m ) of matrix valued rapidly decreasing distributions on ℝⁿ. It is proved that G C ' ( ; M m × m ) is the generating distribution of an i.d.c.s. if and only if the operator t m × m - G on 1 + n satisfies the Petrovskiĭ condition for forward evolution. Some consequences are discussed.

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