Decomposing and twisting bisectorial operators

Tom 197 / 2010

Wolfgang Arendt, Alessandro Zamboni Studia Mathematica 197 (2010), 205-227 MSC: Primary 47D06; Secondary 47A60. DOI: 10.4064/sm197-3-1


Bisectorial operators play an important role since exactly these operators lead to a well-posed equation $u'(t)=Au(t)$ on the entire line. The simplest example of a bisectorial operator $A$ is obtained by taking the direct sum of an invertible generator of a bounded holomorphic semigroup and the negative of such an operator. Our main result shows that each bisectorial operator $A$ is of this form, if we allow a more general notion of direct sum defined by an unbounded closed projection. As a consequence we can express the solution of the evolution equation on the line by an integral operator involving two semigroups associated with $A$.


  • Wolfgang ArendtInstitute of Applied Analysis
    University of Ulm
    Helmholtzstr. 18
    89081 Ulm, Germany
  • Alessandro ZamboniDipartimento di Matematica
    Università degli Studi di Parma
    via G. P. Usberti 53//A
    43100 Parma, Italy

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