Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques Vol. CXXII, No. 26, pp. 53–74 (2001) 

A class of exponentially bounded distribution semigroupsM. Mijatovic and S. PilipovicInstitute of Mathematics, University of Novi Sad, Trg Dositeja Obradovica 4, 21000 Novi Sad, YugoslaviaAbstract: 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 quasidistribution semigroups. In fact we show that our class of distribution semigroup is identical to WangKunstmann'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. Keywords: distribution semigroups, integrated semigroups Classification (MSC2000): 47D03 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 20 Aug 2001. This page was last modified: 20 Jun 2011.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
