International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 44, Pages 2347-2355

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

Received 30 July 2003

Copyright © 2004 Carlo Cattani and Luis M. Sánchez Ruiz. 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 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.