About the Optimal Replacement of the Lebesque Constant Fourier Operator by a Logarithmic Function

Abstract

The Lebesgue constant, corresponding to the classical Fourier operator is approaching a two-parameter family of logarithmic functions. The optimal values of these parameters are found in which the best uniform approximation of the Lebesgue constant a well-defined function of this family is achieved. We considered the case when corresponding to these functions the remaining members are strictly decreasing.