Analysis establishes convergence of singular integral operators including Gauss-Weierstrass in multiple contexts, suggesting indeed their significance in approximation theory.
In this article, we continue the study of approximation of various smooth singular integral operators. This time the foundation of our research is a trigonometric Taylor’s formula. We establish the convergence of our operators to the unit operator with rates via Jackson type inequalities engaging the first modulus of continuity. Of interest here is a residual appearing term. Note that our operators are not positive. Our results are pointwise and uniform. The studied operators here are of the following types: Gauss-Weierstrass, Poisson-Cauchy and trigonometric.
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George A. Anastassiou (2024) studied this question.
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