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Distribution semigroups on function spaces with singularities at zero. (English) Zbl 1199.47181
The authors analyze semigroups defined on test function spaces, consisting of functions with appropriate integrability conditions at zero. Let $$\mathcal F_r$$, $$r\in \mathbb{R}$$, be a scale of Fréchet spaces which are completions of the distribution space $$\mathcal D((0,\infty))$$ under a fixed sequence of seminorms. The authors characterize $$r$$-strong distribution semigroups over $$\mathcal F_r$$ with an additional pointwise structural assumption. In such a way, the authors supplement the results on distribution semigroups on function spaces with singularities at zero.
##### MSC:
 47D06 One-parameter semigroups and linear evolution equations 47D62 Integrated semigroups
##### Keywords:
integrated semigroups; distribution semigroups
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