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<p>We study a nonlinear version of the classical generalized sampling series within the space of functions of bounded variation. In particular, by means of such operators, in the case of kernels of product and averaged type, we obtain a variation-diminishing type estimate and a convergence result. The problem of the rate of approximation is also addressed.</p>

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Approximation methods in BV for nonlinear generalized sampling series

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月10日

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  • Laura Angeloni,
  • Federica Vici

摘要

We study a nonlinear version of the classical generalized sampling series within the space of functions of bounded variation. In particular, by means of such operators, in the case of kernels of product and averaged type, we obtain a variation-diminishing type estimate and a convergence result. The problem of the rate of approximation is also addressed.