ON TWO CONJECTURES INSEGAL-BARGMANN ANALYSIS

摘要

I present a review of two conjectures, each one about an inequality in the Segal-Bargmann space in the case when the dimension of the underlying phase space is finite. One concerns a reverse log-Sobolev inequality, and the other concerns a Hirschman inequality. If either conjecture is true, it allows us to prove the corresponding inequality in the case of infinite dimensional phase space.