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.

翻译：本文针对分段连续多项式相关的$C^0$正交多分辨率分析，给出了其尺度函数以超几何函数表示的显式表达式。推导了这些函数的梅林变换及其傅里叶变换的封闭公式。文中引入并讨论了几类新的多分辨率分析，其尺度函数的系数为有理数。