Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics

In this paper we construct certain continuous piecewise rational wavelets on arbitrary spherical triangulations, giving explicit expressions of these wavelets. Our wavelets have small support, a fact which is very important in working with large amounts of data, since the algorithms for decomposition, compression and reconstruction deal with sparse matrices. We also give a quasi-interpolant associated to a given triangulation and study the approximation error. Some numerical examples are given to illustrate the efficiency of our wavelets.

We give a method for constructing certain orthogonal matrices of arbitrary dimension. As application, we construct orthonormal piecewise constant wavelet bases on two-dimensional domains.