On the Dirichlet Kernels with Respect to Certain Special Representative Product Systems

Abstract

The Fourier analysis uses the calculations with kernel functions from the very beginning. The maximal values of the n th Dirichlet kernels divided by n for the Walsh–Paley, “classical” Vilenkin, and some other systems are 1. In the paper, we deal with some more general systems and use the accumulated results to develop the methods aimed at determination of the properties of specific systems. In these cases, the situation with \( \frac{D_n}{n} \) may be different.