Abstract
Let Γ be a set of three integers and let
be the space of 2π-periodic functions with spectrum in Γ endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T ∈
and prove that x is unique unless |T| has an axis of symmetry. This enables us to compute the exposed and the extreme points of the unit ball of
, 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
. We obtain in particular the Sidon constant of Γ.
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Neuwirth, S. The maximum modulus of a trigonometric trinomial. J Anal Math 104, 371–396 (2008). https://doi.org/10.1007/s11854-008-0028-2
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DOI: https://doi.org/10.1007/s11854-008-0028-2