The L1 norm of the generalized de la Vallee Poussin kernel

TL;DR

This paper investigates the L1 norm of a generalized de la Vallée Poussin kernel, showing it remains constant across certain families and providing exact values, thus advancing understanding of these kernels in harmonic analysis.

Contribution

It determines the exact L1 norm of a generalized de la Vallée Poussin kernel, revealing its constancy in families of delayed means, which was previously unknown.

Findings

L1 norms are constant in families of delayed means

Exact values of the L1 norm are computed

Provides new insights into the structure of de la Vallée Poussin kernels

Abstract

Charles de la Vall'ee Poussin defined two different kernels that bear his name. This paper considers the one are a linear combinations of two Fej'er kernels, which are known as the delayed means. We show that the $L^1$ norms are constant in families of delayed means, and determine the exact value