Global Maximizers for the Sphere Adjoint Fourier Restriction Inequality

We show that constant functions are global maximizers for the adjoint Fourier restriction inequality for the sphere.Comment: corrected few typos and the value of the best constant of the estimate which was not computed correctly in the first draw of the pape

Maximizers for the Strichartz inequality

We compute explicitely the best constants and, by solving some functional equations, we find all maximizers for homogeneous Strichartz estimates for the Schrodinger equation and for the wave equation in the cases when the Lebesgue exponent is an even integer.Comment: 32 pages (uses Tikz/PGF code for pictures). Simplified the computation of some integrals using invariance properties. Corrected a wrong proof of a lemma (thanks to the referee