Classes of distribution semigroups

Tom 187 / 2008

Peer Christian Kunstmann, Modrag Mijatovi/c, Stevan Pilipovi/c Studia Mathematica 187 (2008), 37-58 MSC: 47D06, 47D62. DOI: 10.4064/sm187-1-2

Streszczenie

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.

Autorzy

  • Peer Christian KunstmannMathematisches Institut I
    Universität Karlsruhe
    Englerstr. 2
    D-76128 Karlsruhe, Germany
    e-mail
  • Modrag Mijatovi/cDepartment of Mathematics
    and Informatics
    University of Novi Sad
    Trg D. Obradovi/ca 4
    21 000 Novi Sad, SCG
  • Stevan Pilipovi/cDepartment of Mathematics
    and Informatics
    University of Novi Sad
    Trg D. Obradovi/ca 4
    21 000 Novi Sad, SCG
    e-mail

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