Sobre os teoremas de Bohnenblust-Hille.

Abstract

The Bohnenblust-Hille theorems, proved in 1931 in the prestigious journal Annals of Mathematics, were used as very useful tools in the solution of the famous "Bohr's absolute convergence problem". After a long time overlooked, these theorems have been explored in the recent years. Last quinquennium experienced the rising of several works dedicated to estimate the Bohnenblust-Hille constants and also unexpected connections with Quantum Information Theory appeared. There are in fact four cases to be investigated: polynomial (real and complex cases) and multilinear (real and complex cases). We can summarize in a sentence the main information from the recent preprints: the Bohnenblust-Hille constants are, in general, extraordinarily smaller than the rst estimates predicted. In this work, we present some of our small contributions to the study of the constants of the inequalities Bohnenblust-Hille.