Advances in Difference Equations
Volume 2009 (2009), Article ID 290625, 14 pages
Maximal Regularity of the Discrete Harmonic Oscillator Equation
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.
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 -maximal regularity—or well posedness—solely in terms of -boundedness properties of the resolvent operator involved in the equation.