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<p>We study the convergence of Two-point Padé approximants to Herglotz-Riesz transforms associated with a finite positive Borel measure supported on an arc of the unit circle. In addition, we obtain the corresponding convergence of the approximants to the Herglotz-Riesz transform with rational perturbation with poles outside the arc. The exact rate of convergence is obtained.</p>

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Padé approximation to Herglotz-Riesz transforms on an arc

  • 期刊论文

  • 发表日期：

    2025年11月5日

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  • Adhemar Bultheel,
  • Carlos Díaz Mendoza

摘要

We study the convergence of Two-point Padé approximants to Herglotz-Riesz transforms associated with a finite positive Borel measure supported on an arc of the unit circle. In addition, we obtain the corresponding convergence of the approximants to the Herglotz-Riesz transform with rational perturbation with poles outside the arc. The exact rate of convergence is obtained.