12 citations · 29 across the 12 of their papers we have counts for
13 papers · 1 filter
Uniformly Bounded Orthonormal Bases of Homogeneous Polynomials on the Complex Sphere
Felipe Gonçalves, João P. Ferreira, Maksym Radziwiłł
We resolve the long-standing problem of Rudin concerning uniformly bounded orthonormal bases of homogeneous polynomials on complex unit spheres. Specifically, we show that for ever…
A component-wise inequality for permutation matches
Felipe Gonçalves
Motivated by the recent paper [Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution, arXiv:2609.29882],…
The Hörmander--Bernhardsson function in higher dimensions
Felipe Gonçalves, Danylo Radchenko, Antonio Pedro Ramos
We study the problem of finding the norm of the point evaluation operator in the Paley--Wiener space $PW^{1}(\r^d)$, consisting of -variable functions of spherical exponential t…
A note on discrete Heisenberg uniqueness pairs for the parabola
Felipe Gonçalves, João P. G. Ramos
We discuss on Heisenberg uniqueness pairs for the parabola given by discrete sequences along straight lines. Our method consists in linking the problem at hand with recent uniquene…
Strichartz Estimates with Broken Symmetries
Felipe Gonçalves, Don Zagier
In this note we study the eigenvalue problem for a quadratic form associated with Strichartz estimates for the Schrödinger equation, proving in particular a sharp Strichartz inequa…
Local maximizers of adjoint Fourier restriction estimates for the cone, paraboloid and sphere
Felipe Gonçalves, Giuseppe Negro
We show that, possibly after a compactification of spacetime, constant functions are local maximizers of the Tomas-Stein adjoint Fourier restriction inequality for the cone and par…
New Sign Uncertainty Principles
Felipe Gonçalves, Diogo Oliveira e Silva, João P. G. Ramos
We prove new sign uncertainty principles which vastly generalize the recent developments of Bourgain, Clozel & Kahane and Cohn & Gonçalves, and apply our results to a variety of sp…
On regularity and mass concentration phenomena for the sign uncertainty principle
Felipe Gonçalves, Diogo Oliveira e Silva, João P. G. Ramos
The sign uncertainty principle of Bourgain, Clozel & Kahane asserts that if a function and its Fourier transform are nonpositive at the…
An optimal uncertainty principle in twelve dimensions via modular forms
Henry Cohn, Felipe Gonçalves
We prove an optimal bound in twelve dimensions for the uncertainty principle of Bourgain, Clozel, and Kahane. Suppose is an integrable fun…
A Sharpened Strichartz Inequality For Radial Functions
Felipe Gonçalves
We prove a sharpened version of the Strichartz inequality for radial solutions of the Schrödinger equation in . We establish an improved upper bound…
Hermite polynomials, linear flows on the torus, and an uncertainty principle for roots
Felipe Gonçalves, Diogo Oliveira e Silva, Stefan Steinerberger
We study a recent result of Bourgain, Clozel and Kahane, a version of which states that a sufficiently nice function that coincides with its F…
Extremal problems in de Branges spaces: the case of truncated and odd functions
Emanuel Carneiro, Felipe Gonçalves
In this paper we find extremal one-sided approximations of exponential type for a class of truncated and odd functions with a certain exponential subordination. These approximation…
One-sided Band-limited Approximations of Some Radial Functions
Felipe Gonçalves, Michael Kelly, José Madrid
We construct majorants and minorants of a Gaussian function in Euclidean space that have Fourier transforms supported in a box. The majorants that we construct are shown to be extr…