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In this article we continue with the study of smooth Gauss-Weierstrass, Poisson-Cauchy and Trigonometric singular integral operators that started in [3], see there chapters 10–14. This time the foundation of our research is a trigonometric Taylor’s formula. We establish the univariate \(L_{p}\) convergence of our operators to the unit operator with rates via Jackson type inequalities involving the first \(L_{p}\) modulus of continuity. Of interest here is a residual appearing term. Note that our operators are not positive.

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Trigonometric Deduced \(L_p\) Degree of Approximation by Various Smooth Singular Integral Operators

  • 会议论文

  • 发表日期：

    2025年

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  • George A. Anastassiou

摘要

In this article we continue with the study of smooth Gauss-Weierstrass, Poisson-Cauchy and Trigonometric singular integral operators that started in [3], see there chapters 10–14. This time the foundation of our research is a trigonometric Taylor’s formula. We establish the univariate \(L_{p}\) convergence of our operators to the unit operator with rates via Jackson type inequalities involving the first \(L_{p}\) modulus of continuity. Of interest here is a residual appearing term. Note that our operators are not positive.