Discrete differential operators in multidimensional Haar wavelet spaces. (English) Zbl 1075.39008

Cattani, Carlo; Sánchez Ruiz, Luis M.

Int. J. Math. Math. Sci. 2004, No. 41-44, 2347-2355 (2004).

Authors’ summary: 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.

MSC:

39A12	Discrete version of topics in analysis
35A35	Theoretical approximation in context of PDEs
42C40	Nontrigonometric harmonic analysis involving wavelets and other special systems

Keywords:

discrete differential operators; Haar wavelet basis; interpolating method; regularization