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<p>We present explicit representations in terms of hypergeometric functions for the scaling functions in the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(C^0\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>0</mn> </msup> </math></EquationSource> </InlineEquation> 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.</p>

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Compactly Supported, Orthogonal, Continuous Piecewise Polynomial Multiresolution Analysis

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月7日

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  • Lidia Fernández,
  • Jeffrey S. Geronimo,
  • Plamen Iliev

摘要

We present explicit representations in terms of hypergeometric functions for the scaling functions in the \(C^0\) 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.