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<p>A systematic and comprehensive study of <i>p</i>-adic refinement equations and cascade algorithm associated with a finitely supported refinement filter is carried out in this paper. The <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( L_{q} \)</EquationSource> </InlineEquation>-convergence of the cascade algorithm is characterized in terms of the <i>q</i>-norm joint spectral radii of a collection of operators associated with the refinement filter. Also, the smoothness of complex-valued functions on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( \mathbb {Q}_{p} \)</EquationSource> </InlineEquation>&#xa0; is investigated.</p>

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Convergence of subdivision schemes and smoothness of refinable functions on p-adic fields

  • 期刊论文

  • 发表日期：

    2026年5月8日

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  • N. Athira,
  • M. C. Lineesh

摘要

A systematic and comprehensive study of p-adic refinement equations and cascade algorithm associated with a finitely supported refinement filter is carried out in this paper. The \( L_{q} \) -convergence of the cascade algorithm is characterized in terms of the q-norm joint spectral radii of a collection of operators associated with the refinement filter. Also, the smoothness of complex-valued functions on \( \mathbb {Q}_{p} \)   is investigated.