Polarization of an inequality

Details Polarization of an inequality Polarization of an inequality

2009-05-09

arxiv.org/abs/0905.1426v2

Mathematics

Classical Analysis and ODEs

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

Scientific paper

We generalize a previous inequality related to a sharp version of the Littlewood conjecture on the minimal $L_1$-norm of $N$-term exponential sums $f$ on the unit circle. The new result concerns replacing the expression $\log(1+t|f|^2)$ with $\log (\sum_{k=1}^K t_k|f_{k}|^2)$. 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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