Compactly supported, orthogonal, continuous piecewise polynomial multiresolution analysis
Provides theoretical tools for constructing orthogonal wavelet bases with compact support and continuity, relevant to signal processing and numerical analysis.
The authors derive explicit representations and closed formulas for scaling functions in C0 orthogonal multiresolution analyses of piecewise continuous polynomials, and introduce new analyses with rational coefficients.
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.