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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-3-1,
author = {Wolfgang Arendt and Alessandro Zamboni},
title = {Decomposing and twisting bisectorial operators},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {205-227},
zbl = {1194.47046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-3-1}
}
Wolfgang Arendt; Alessandro Zamboni. Decomposing and twisting bisectorial operators. Studia Mathematica, Tome 196 (2010) pp. 205-227. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-3-1/