  We show that B-spline quarks and the associated quarklets fit into the theory
of biorthogonal multiwavelets. Quark vectors are used to define sequences of
subspaces $ V_{p,j} $ of $ L_{2}(\mathbb{R}) $ which fulfill almost all
conditions of a multiresolution analysis. Under some special conditions on the
parameters they even satisfy all those properties. Moreover we prove that
quarks and quarklets possess modulation matrices which fulfill the perfect
reconstruction condition. Furthermore we show the existence of generalized dual
quarks and quarklets which are known to be at least compactly supported
tempered distributions from $\mathcal{S}'(\mathbb{R})$. Finally we also verify
that quarks and quarklets can be used to define sequences of subspaces $
W_{p,j} $ of $ L_{2}(\mathbb{R}) $ that yield non-orthogonal decompositions of
$ L_{2}(\mathbb{R}) $.
