Polarization of an inequality

2009/05/09 by Ivo Klemes, Klemes, Ivo
Mathematics · #15A15 #15A42 #42A32 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory (math.SP) #math.CA #math.SP #msc:15A15 #msc:15A42 #msc:42A32

paper · pdf · doi:10.48550/arxiv.0905.1426

9 pages. Updated references and remarks in section 3. Accepted in Math. Inequalities and Appl

arxiv created 2011/01/09 · arxiv updated 2011/01/11

Abstract

We generalize a previous inequality related to a sharp version of the Littlewood conjecture on the minimal L₁-norm of N-term exponential sums f on the unit circle. The new result concerns replacing the expression log(1+t|f|²) with log (∑_k=1^K t_k|f_k|²). The proof occurs on the level of finite Toeplitz matrices, where it reduces to an inequality between their polarized determinants (or "mixed discriminants").

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