Approximation of the Lebesgue Constant of the Fourier Operator by a Logarithmic-Fractional-Rational Function

Abstract

The Lebesgue constant of the classical Fourier operator is uniformly approximated by a logarithmic-fractional-rational function depending on three parameters; they are defined using the specific properties of logarithmic and rational approximations. A rigorous study of the corresponding residual term having an indefinite (nonmonotonic) behavior has been carried out. The obtained approximation results strengthen the known results by more than two orders of magnitude.