Compactly supported multi-wavelets (Q2901930)

The purpose of this paper is to give a generalization of the orthogonal compactly supported wavelets which have been constructed by Daubechies in the one-dimensional case. New compactly supported multi-wavelets in \(L^2(\mathbb R^d), d \geq 2\), are based on the one-dimensional functions, when \(d = 1\). It is demonstrated that some methods, which are useful in the construction of wavelets with compact supports at \(d = 1\), can be adapted to higher-dimensional cases. The Schmidt orthogonalization method is used, but an explanation of the reservation of the compact supports of the functions is not given. The triangular grids are not used in the construction of new functions.