Classes of distribution semigroups
Volume 187 / 2008
Studia Mathematica 187 (2008), 37-58
MSC: 47D06, 47D62.
DOI: 10.4064/sm187-1-2
Abstract
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.
