Author

Felipe Gonçalves

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Preprint Aug 2026

The H\"ormander--Bernhardsson function in higher dimensions

We study the problem of finding the norm of the point evaluation operator in the Paley--Wiener space $PW^{1}(\r^d)$, consisting of $d$-variable functions of spherical exponential type that are integrable on $\r^d$. The extremal functions can be taken radial, which naturally leads us to consider a related extremal probl...

Felipe Gonçalves, D. Radchenko, Antonio Pedro Ramos · 0 citations

Preprint Sep 2026

Gaussians Do Not Always Maximize Mixed-Norm Strichartz Inequalities for the Schr\"odinger Equation

We investigate the maximization problem for the family of mixed-norm Strichartz inequalities for the Schr\"odinger equation, $\|e^{-it\Delta/2}f\|_{L_t^qL_{\boldsymbol{x}}^r(\mathbb{R}^{1+d})}\le C_{q,r}\lVert f\rVert_{L^2(\mathbb{R}^d)}$, with $2/q+d/r=d/2$, $q,r\geq 2$, and thus $r\leq 2d/(d-2)$ if $d\geq 3$. We show...

Felipe Gonçalves, Giuseppe Negro, D. O. E. Silva · 0 citations