Decomposing and twisting bisectorial operators

Wolfgang Arendt, and Alessandro Zamboni. "Decomposing and twisting bisectorial operators." Studia Mathematica 197.3 (2010): 205-227. <http://eudml.org/doc/285550>.

@article{WolfgangArendt2010,
abstract = {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.},
author = {Wolfgang Arendt, Alessandro Zamboni},
journal = {Studia Mathematica},
keywords = {bisectorial operators; unbounded cosed projections},
language = {eng},
number = {3},
pages = {205-227},
title = {Decomposing and twisting bisectorial operators},
url = {http://eudml.org/doc/285550},
volume = {197},
year = {2010},
}

TY - JOUR
AU - Wolfgang Arendt
AU - Alessandro Zamboni
TI - Decomposing and twisting bisectorial operators
JO - Studia Mathematica
PY - 2010
VL - 197
IS - 3
SP - 205
EP - 227
AB - 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.
LA - eng
KW - bisectorial operators; unbounded cosed projections
UR - http://eudml.org/doc/285550
ER -