Geodesic
A class of exponentially bounded distribution semigroups
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 26 (2001), p. 53 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

A structural theorem for a vector valued exponentially bounded distribution is used for introducing and studyng of a class distribution semigroups. An infinitesimal generator of such a semigroup is not necessarily densely defined, but if it is the case, then it corresponds to a distribution semigroup introduced by Lions. This result is obtained by Wang and Kunstmann for a class of exponentially bounded quasi-distribution semigroups. In fact we show that our class of distribution semigroup is identical to Wang-Kunstmann's one. Our approach is completely different and gives new characterizations. Applications to equations $\displaystyle \frac{\partial u}{\partial t} = Au +f,$ where $A$ is not necessarily densely defined and $f$ is an exponential vector valued distribution supported by $[0, \infty ),$ are given. This paper is written much before the publishing of Wang's and Kunstmann's paper but because of various reasons it is published with a very long delay. Here it is given in the primary version as an original approach although some parts are consequences of published results of Wang and Kunstmann.
Classification : 47D03
Keywords: distribution semigroups, integrated semigroups 
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     title = {A class of exponentially bounded distribution semigroups},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {53 },
     publisher = {mathdoc},
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     year = {2001},
     zbl = {1004.47024},
     language = {en},
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M. Mijatović; S. Pilipović. A class of exponentially bounded distribution semigroups. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 26 (2001), p. 53 . http://geodesic.mathdoc.fr/item/BASS_2001_26_a3/