Order Estimates of Smallest Norms, with Respect to the Choice of N Harmonics, of Derivatives of the Dirichlet and Favard Kernels

Abstract

The Dirichlet kernel is defined for periodic functions of several variables; it consists of harmonics and has minimal order of the norm with respect to the choice of harmonics of the mixed Weyl derivative in the space . A similar problem on the minimal order of the norm is solved for the Favard kernel. Both problems generalize to the case of several derivatives.