MRA gives rise to a wavelet basis. Wavelet theory is very young. It blends beautifully different branches of Mathematics. MRA assumes that there is only one scaling function. We make a step forward and allow several of them.
New object is called a multi-scaling function.
It has new features determined by the matrix structure of the dilation equation. For example, a multi-scaling function can combine orthogonality, symmetry and high approximation order while a scalar scaling function cannot. Using this technique we suggest an efficient way to construct biorthogonal multiwavelet bases with approximation and symmetry. As an example we present a biorthogonal pair of smooth bases built from piecewise polynomial finite elements. We argue why multiwavelets are promising in practice, describe possible applications and point out difficulties of their implementation.