Une propriété de concavité pour l'équation de la chaleur en dimension un

It is proved that, if µ is a positive measure on $\mathbb{R}$ of positive type, the function (Gμ)(t)=∫$_\mathbb{R}${exp(-tx$^{2}$)dμ(x) satisfies the "J-concavity" property, a collection of differential inequalities of order two. Consequently, for the solutions of the heat equation on $\mathbb{R}$ with positive initial condition, the energy functional satisfies the same property; and there is a similar result for the heat equation on $\mathbb{R/Z}$. From this follows a new proof of the theorem of Cohn and Kumar asserting the universal optimality of the lattice $\mathbb{Z}$ in dimension one.