6 papers
Sharp Lower Bounds for Sumsets in Hypercubes
Felipe Gonçalves, Danylo Radchenko
We prove a sharp lower bound for the cardinality of sumsets of subsets of confined to a hypercube, resolving in strong form a conjecture that was made explicit by Be…
On the Uniqueness of the Norton-Sullivan Quasiconformal extension
José Afonso Barrionuevo, Felipe Gonçalves, José Victor Medeiros +1
We show that the extension map \[ \mathcal{E}_{NS}(f)(z)=\frac{f(x+y)+f(x-y)}{2}+i\frac{f(x+y)-f(x-y)}{2}\mbox{ for all }z=x+iy\in\mathbb{H}\,, \] defined by Norton and Sullivan in…
A classification of Fourier summation formulas and crystalline measures
Felipe Gonçalves
We completely classify Fourier summation formulas, and in particular, all crystalline measures with quadratic decay. Our classification employs techniques from almost periodic func…
On a Sharp Fourier Extension Inequality on the Circle with Lacunary Spectrum
Felipe Gonçalves, João Paulo Ferreira
We prove a sharp Fourier extension inequality on the circle for the Tomas-Stein exponent for functions whose spectrum satisfies .
A Complete Classification of Fourier Summation Formulas on the real line
Felipe Gonçalves, Guilherme Vedana
We completely classify Fourier summation formulas of the form that hold for any test function …
Sign uncertainty principles and low-degree polynomials
Henry Cohn, Dingding Dong, Felipe Gonçalves
We prove an asymptotically sharp version of the Bourgain-Clozel-Kahane and Cohn-Gonçalves sign uncertainty principles for polynomials of sublinear degree times a Gaussian, as the…