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The study presents new scaling functions and transforms in piecewise polynomial analyses, indicating advancements in mathematical frameworks.
We present explicit representations in terms of hypergeometric functions for the scaling functions in the C⁰ 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.
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Fernández et al. (2026) studied this question.
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