Biorthogonal multiresolution analysis on a triangle and applications

We present in this paper new constructions of biorthogonal multiresolution analysis on the triangle ∆. We use direct method based on the tensor product to construct dual scaling spaces on ∆. Next, we construct the associated wavelet spaces and we prove that the associated wavelets have compact support and preserve the original regularity. Finally, we describe some regular results which are very useful to establish the norm equivalences. As applications, we prove that the wavelet bases constructed in this paper are adapted for the study of the Sobolev spaces H 0(∆) and H (∆) (s ∈ N) and are easy to implement.