Affine system of Walsh type. Completeness and minimality

The question on completeness and minimality of Walsh affine systems is considered. On the basis of functional-analytical structure of multishift in Hilbert space, which being the generalized analogue of the operator of simple one-side shift and closely connected with Cuntz algebra representations, we give definition of Walsh affine system. Various criteria and tests of completeness of affine systems of functions are established. A biorthogonal conjugate system is found and its completeness is proved.