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 (non-monotonic) behavior has been carried out. The obtained approximation results strengthen the known results by more than two orders of magnitude.
Keywords:Lebesgue constant of the Fourier operator, fractional rational function, asymptotic formula, two-way estimation of the Lebesgue constant, extreme problem, approximation error.