B-spline quarklets and biorthogonal multiwavelets

In this paper, we show that B-spline quarks and the associated quarklets fit into theory of biorthogonal multiwavelets. Quark vectors are used to define sequences subspaces [Formula: see text] which fulfill almost all conditions a multiresolution analysis. Under some special on parameters, they even satisfy those properties. Moreover, prove possess modulation matrices perfect reconstruction condition. Furthermore, existence generalized dual known be at least compactly supported tempered distributions from text]. Finally, also verify can yield non-orthogonal decompositions