Maximal regularity of evolution equations on discrete time scales
Date
2005
Authors
Portal, Pierre
Journal Title
Journal ISSN
Volume Title
Publisher
Academic Press
Abstract
We consider the question of Lp-maximal regularity for inhomogeneous Cauchy problems in Banach spaces using operator-valued Fourier multipliers. This follows results by L. Weis in the continuous time setting and by S. Blunck for discrete time evolution equations. We generalize the later result to the case of some discrete time scales (discrete problems with nonconstant step size). First we introduce an adequate evolution family of operators to consider the general problem. Then we consider the case where the step size is a periodic sequence by rewriting the problem on a product space and using operator matrix valued Fourier multipliers. Finally we give a perturbation result allowing to consider a wider class of step sizes.
Description
Keywords
Keywords: Difference equations; Evolution equations in Banach spaces; Operator matrices; Operator-valued Fourier multipliers; Time scales
Citation
Collections
Source
Journal of Mathematical Analysis and Applications
Type
Journal article
Book Title
Entity type
Access Statement
License Rights
Restricted until
2037-12-31
Downloads
File
Description