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Decomposing and twisting bisectorial operators

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Arendt W., Zamboni A.

Studia Mathematica

2010

tom 197

nr 3

205-227

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.

Ograniczanie wyników

1 Studia Mathematica

1 Arendt W.

1 Zamboni A.

1 2010

Wyniki wyszukiwania

Decomposing and twisting bisectorial operators