Maximal regularity of evolution equations on discrete time scales |
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Authors: | Pierre Portal |
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Affiliation: | University of Missouri, Department of Mathematics, Columbia, MO 65201, USA |
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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. |
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Keywords: | Evolution equations in Banach spaces Difference equations Time scales Operator-valued Fourier multipliers Operator matrices |
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