Classes of distribution semigroups

Peer Christian Kunstmann¹ ; Modrag Mijatovi/c² ; Stevan Pilipovi/c²

¹ Mathematisches Institut I Universität Karlsruhe Englerstr. 2 D-76128 Karlsruhe, Germany
² Department of Mathematics and Informatics University of Novi Sad Trg D. Obradovi/ca 4 21 000 Novi Sad, SCG

Studia Mathematica, Tome 187 (2008) no. 1, pp. 37-58

Résumé

We introduce various classes of distribution semigroups distinguished by their behavior at the origin. We relate them to quasi-distribution semigroups and integrated semigroups. A class of such semigroups, called strong distribution semigroups, is characterized through the value at the origin in the sense of /Lojasiewicz. It contains smooth distribution semigroups as a subclass. Moreover, the analysis of the behavior at the origin involves intrinsic structural results for semigroups. To this purpose, new test function spaces and distribution semigroups over these spaces are introduced. We give applications to Schrödinger type equations in the spaces $C_{\rm b}$, $L^\infty$, and BMO with elliptic non-densely defined operators.

Détail

DOI : 10.4064/sm187-1-2

Keywords: introduce various classes distribution semigroups distinguished their behavior origin relate quasi distribution semigroups integrated semigroups class semigroups called strong distribution semigroups characterized through value origin sense lojasiewicz contains smooth distribution semigroups subclass moreover analysis behavior origin involves intrinsic structural results semigroups purpose test function spaces distribution semigroups these spaces introduced applications schr dinger type equations spaces infty bmo elliptic non densely defined operators