International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 41-44, Pages 2347-2355
doi:10.1155/S0161171204307234
Discrete differential operators in multidimensional Haar wavelet spaces
Carlo Cattani1
and Luis M. Sánchez Ruiz2
1Dipartimento di Scienze Farmaceutiche (DiFARMA), Università degli Studi di Salerno, Via Ponte Don Melillo, Invariante 11/C, Fisciano (Salerno) 84084, Italy
2Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingeniería de Diseño (ETSID), Universidad Politécnica de Valencia, Valencia 46022, Spain
Abstract
We consider a class of discrete differential operators acting on multidimensional Haar wavelet basis with the aim of finding wavelet approximate solutions of partial differential problems. Although these operators depend on the interpolating method used for the Haar wavelets regularization and the scale dimension space, they can be easily used to define the space of approximate wavelet solutions.