The maximum modulus of a trigonometric trinomial
نویسنده
چکیده
Let Λ be a set of three integers and let CΛ be the space of 2π-periodic functions with spectrum in Λ endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T ∈ CΛ 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 CΛ, 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 CΛ. We obtain in particular the Sidon constant of Λ.
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