The modulus semigroup for linear delay equations II
Abstract
The main purpose of this paper is describing the generator of the modulus semigroup of the
-semigroup associated with the delay equation (Error rendering LaTeX formula) in the Banach lattice
, where X is a Banach lattice with order continuous norm. As a preparation it is shown that
is a sublattice of
, for
. A further preparation is the computation of the modulus of the operator L appearing above. Also, we establish a result concerning the existence of the modulus semigroup for
-semigroups acting in
-spaces.
![C<sub>0</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/4034737f198b083e7a0ec47e6b0c32e6.png)
![X L<sub>p</sub>(-h,0; X)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/f91f4c81068e5d76cfbb79adb36638be.png)
![W<sup>1</sup><sub>p</sub>(a,b; X)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/bdf0213039b19ce8958c3e873d8bdc6d.png)
![L<sub>p</sub>(a,b; X)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/13ccbf666b56f2d3dc2fd86dad904317.png)
![1 ≤ p < ∈fty](http://siba-ese.unile.it/plugins/generic/latexRender/cache/7790de9222eef1d37827108a0bdb1d7b.png)
![C<sub>0</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/4034737f198b083e7a0ec47e6b0c32e6.png)
![KB](http://siba-ese.unile.it/plugins/generic/latexRender/cache/ab57fd0432e25d5b3013133a1c910d56.png)
DOI Code:
10.1285/i15900932v25n2p191
Keywords:
Functional differential equation; Modulus semigroup; Perturbation theory
Classification:
47D06; 34k06; 47B60
Full Text: PDF