Orthogonal polynomial wavelets

Recently algebraic polynomials have been considered as wavelets and handled by wavelet techniques. In the unified approach for the construction of polynomial wavelets by Fischer and Prestin, the actual implementation of decomposition, reconstruction and/or compression schemes required at each level the inversion of generalized Grammian matrices, in general not orthogonal. In this context the present paper works out necessary and sufficient conditions for the polynomial wavelets to be orthogonal to each other. Furthermore it shows how these computable characterizations lead to attractive decomposition and reconstruction algorithms based on orthogonal matrices. Finally the special case of Bernstein--Szego weight functions is studied in detail.