Compactly supported, orthogonal, continuous piecewise polynomial multiresolution analysis

Abstract: We present explicit representations in terms of hypergeometric functions for the scaling functions in the $C^0$ orthogonal multiresolution analyses associated with piecewise continuous polynomials. Closed formulas for the Mellin transform of these functions as well as their Fourier transforms are derived. Some new multiresolution analyses whose scaling functions have coefficients that are rational numbers are introduced and discussed.