Advances in Difference Equations
Volume 2009 (2009), Article ID 290625, 14 pages
doi:10.1155/2009/290625
Maximal regularity of the discrete harmonic oscillator equation
Airton Castro1
, Claudio Cuevas1
and Carlos Lizama3
1Departamento de Matemática, Universidade Federal de Pernambuco, Avenida. Professor. Luiz Freire, S/N, 50540-740 Recife, PE, Brazil
3Departamento de Matemática y Ciencia de la Computacion, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307-Correo 2, 9160000 Santiago, Chile
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.