Interpolating polynomial wavelets on [-1,1]

The paper gives a contribution of wavelet aspects to classical algebraic polynomial approximation theory. Algebraic polynomial interpolating scaling functions and wavelets are constructed by using the interpolating properties of de la Vallée Poussin kernels w.r.t. the four kinds of Chebyshev weights. For the decomposition and reconstruction of a given function the structure of the involved matrices is studied in order to reduce the computational effort by means of fast cosine and sine transforms.