Wavelet bases on a triangle

In the present paper we find new constructions of orthonormal multiresolution analyses on the triangle Δ. In the first one, we describe a direct method to define an orthonormal multiresolution analysis which is adapted for the study of the Sobolev spaces H0s(Δ) (s∈Ns∈N). In the second one, we add boundary conditions for constructing an orthonormal multiresolution analysis which is adapted for the study of the Sobolev spaces Hs(Δ) (s∈Ns∈N). The associated wavelets preserve the original regularity and are easy to implement.