Decomposing and twisting bisectorial operators

• Autorzy: Wolfgang Arendt , Alessandro Zamboni
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 47A60: Functional calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 197
• Numer: 3
• Strony: 205-227

Daty

wydano

2010

Twórcy

autor

Wolfgang Arendt

• Institute of Applied Analysis, University of Ulm, Helmholtzstr. 18, 89081 Ulm, Germany

autor

Alessandro Zamboni

• Dipartimento di Matematica, Università degli Studi di Parma, via G. P. Usberti 53/A, 43100 Parma, Italy

Identyfikatory

DOI

10.4064/sm197-3-1