On Optimal Approximations of the Norm of the Fourier Operator by a Family of Logarithmic Functions

Abstract

The Lebesgue constant corresponding to the classical Fourier operator is approximated by a family of logarithmic functions depending on two parameters. We find optimal values of parameters for which the best uniform approximation of the Lebesgue constant by a specific function of this family is achieved. The case where the corresponding remainder strictly increases is also considered.