Truncating the Fourier transform averaged by means of a generalized Hausdorff operator, we approximate functions and the adjoint to that Hausdorff operator of the given function. We find estimates for the rate of approximation in various metrics in terms of the parameter of truncation and the components of the Hausdorff operator. Explicit rates of approximation of functions and comparison with approximate identities are given in the case of continuous functions from the class $\text {Lip }\alpha $ .

中文翻译：

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通过 Hausdorff 算子逼近

通过广义 Hausdorff 算子截断傅里叶变换的平均值，我们近似函数和给定函数的 Hausdorff 算子的伴随。我们根据截断参数和 Hausdorff 算子的分量找到了各种度量中的近似率估计值。在类$\text {Lip }\alpha $ 的连续函数的情况下，给出了函数逼近的显式率以及与近似恒等式的比较 。