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

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home


Pick a mirror


A class of exponentially bounded distribution semigroups

M. Mijatovic and S. Pilipovic

Institute of Mathematics, University of Novi Sad, Trg Dositeja Obradovica 4, 21000 Novi Sad, Yugoslavia

Abstract: 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.

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
© 2001–2011 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition