The maximum modulus of a trigonometric trinomial

Details The maximum modulus of a trigonometric trinomial The maximum modulus of a trigonometric trinomial

2007-03-08

arxiv.org/abs/math/0703236v1

Mathematics

Functional Analysis

Scientific paper

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.

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