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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.

Operator-Valued Ultradistributions in the Spectral Theory.

Ioana Cioranescu (1976)

Mathematische Annalen

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On alternative functional equations. (Short Communication).

On representation of temperate distributions

On some boundary value problems for ordinary linear differential equations of second order in the Colombeau algebra

On vector measures and distributions

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

Operator-Valued Ultradistributions in the Spectral Theory.

Currently displaying 1 – 6 of 6