17 citations · 18 across the 9 of their papers we have counts for
12 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 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 , wher…
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…
Sharp Fourier Extension on the Circle Under Arithmetic Constraints
Valentina Ciccone, Felipe Gonçalves
We establish a sharp adjoint Fourier restriction inequality for the end-point Tomas-Stein restriction theorem on the circle under a certain arithmetic constraint on the support set…
A Universality Law For Sign Correlations of Eigenfunctions of Differential Operators
Felipe Gonçalves, Diogo Oliveira e Silva, Stefan Steinerberger
We establish a universality law for sequences of functions satisfying a form of WKB approximation on compact intervals. This includes eigenfunctions of…
A Note on Band-limited Minorants of an Euclidean Ball
Felipe Gonçalves
We study the Beurling-Selberg problem of finding band-limited -functions that lie below the indicator function of an Euclidean ball. We compute the critical radius of the supp…
Orthogonal Polynomials and Sharp Estimates for the Schrödinger Equation
Felipe Gonçalves
In this paper we study sharp estimates for the Schrödinger operator via the framework of orthogonal polynomials. We use spherical harmonics and Gegenbauer polynomials to prove a ne…
The Beurling-Selberg Box Minorant Problem via Linear Programming Bounds
Jacob Carruth, Noam Elkies, Felipe Gonçalves +1
In this paper we investigate a high dimensional version of Selberg's minorant problem for the indicator function of an interval. In particular, we study the corresponding problem o…
A Central Limit Theorem for Operators
Felipe Gonçalves
We prove an analogue of the Central Limit Theorem for operators. For every operator defined on we construct a sequence of operators defined on $\mathbb{C}…
Interpolation Formulas With Derivatives in De Branges Spaces
Felipe Gonçalves
The purpose of this paper is to prove an interpolation formula involving derivatives for entire functions of exponential type. We extend the interpolation formula derived by J. Vaa…