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<p>This article gives a generalization of biorthogonal wavelets to the field of <i>p</i>-adic numbers <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {Q}_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Q</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>. Biorthogonal systems provide flexibility in the representation of a function. Dual MRA is discussed. Two MRAs are said to be dual of each other if translates of the corresponding scaling functions form a biorthogonal system. Characteristics of projection operators associated with dual MRAs are studied, and a characterization of biorthogonal wavelets is given in terms of dual orthonormal basis.</p>

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Dual multiresolution analysis on \(\mathbb {Q}_p\)

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Debasis Haldar

摘要

This article gives a generalization of biorthogonal wavelets to the field of p-adic numbers \(\mathbb {Q}_p\) Q p . Biorthogonal systems provide flexibility in the representation of a function. Dual MRA is discussed. Two MRAs are said to be dual of each other if translates of the corresponding scaling functions form a biorthogonal system. Characteristics of projection operators associated with dual MRAs are studied, and a characterization of biorthogonal wavelets is given in terms of dual orthonormal basis.