Abstract
The linear best method for approximating the second derivatives of Hardy class functions defined in the unit circle at zero in accordance with the information about their values in a finite number of points forming a regular polygon is found. The paper is divided into three sections. The first contains the necessary concepts and results from the work of K.Yu. Osipenko. It also recalls some results obtained by S. Ya. Havinson and other authors. In the second section, the error of the best method is calculated, and the corresponding extremal functions are written out. The third proves that the linear best approximation method is unique, and its coefficients are calculated.
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