The maximum modulus of a trigonometric trinomial
Functional Analysis
2017-08-21 v1 Classical Analysis and ODEs
Abstract
Let Lambda be a set of three integers and let C_Lambda be the space of 2pi-periodic functions with spectrum in Lambda endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T in C_Lambda and prove that x is unique unless |T| has an axis of symmetry. This permits to compute the exposed and the extreme points of the unit ball of C_Lambda, to describe how the maximum modulus of T varies with respect to the arguments of its Fourier coefficients and to compute the norm of unimodular relative Fourier multipliers on C_Lambda. We obtain in particular the Sidon constant of Lambda.
Keywords
Cite
@article{arxiv.math/0703236,
title = {The maximum modulus of a trigonometric trinomial},
author = {Stefan Neuwirth},
journal= {arXiv preprint arXiv:math/0703236},
year = {2017}
}