Symmetric polynomials, p-norm inequalities, and certain functionals related to majorization
Abstract
Description
We study a variant of the majorization relation. In particular we consider inequalities involving some Schur-concave symmetric polynomials related to the multinomial expansion. We also discuss how these topics were motivated by conjectures on sharp Lp inequalities between complex exponential sums conjectured by Hardy and Littlewood (still open problems), and why the usual majorization relation does not hold in that context.
LaTeX file, 43 pages (1 figure, included as code in LaTeX file). Previously submitted to a refereed journal in February 2007. This file is a slightly updated version, dated April 2007
LaTeX file, 43 pages (1 figure, included as code in LaTeX file). Previously submitted to a refereed journal in February 2007. This file is a slightly updated version, dated April 2007