Advances in Difference Equations
Volume 2009 (2009), Article ID 290625, 14 pages
doi:10.1155/2009/290625
Research Article

Maximal Regularity of the Discrete Harmonic Oscillator Equation

Airton Castro,1 Claudio Cuevas,1 and Carlos Lizama2

1Departamento de Matemática, Universidade Federal de Pernambuco, Avenida. Professor. Luiz Freire, S/N, 50540-740 Recife, PE, Brazil
2Departamento de Matemática y Ciencia de la Computacion, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307-Correo 2, 9160000 Santiago, Chile

Received 31 October 2008; Revised 27 January 2009; Accepted 9 February 2009

Academic Editor: Mariella Cecchi

Copyright © 2009 Airton Castro et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.