This is an announcement for the paper "The maximum modulus of a trigonometric trinomial" by Stefan Neuwirth.

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.

Archive classification: Functional Analysis; Classical Analysis and ODEs

Mathematics Subject Classification: MSC Primary 30C10, 42A05, 42A45, 46B20; Secondary 26D05, 42A55,

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/math.FA/0703236

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http://arXiv.org/abs/math.FA/0703236

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