6 papers
Rectangles, triangles and Schrödinger waves
Jonathan Bennett, Vjekoslav KovaÄ, Shohei Nakamura +1
Can a finite set of lattice points determine many rectangles and few isosceles triangles? This turns out to be a surprisingly interesting question in combinatorial geometry that we…
Knapp-type obstructions in multilinear fractal Fourier extension
Itamar Oliveira, Ana E. de Orellana
For curved, smooth hypersurfaces, the classical Knapp example shows that the Stein--Tomas theorem, which gives linear Fourier restriction estimates, is sharp. Variants of this exam…
A phase-space approach to weighted Fourier extension inequalities
Jonathan Bennett, Susana Gutierrez, Shohei Nakamura +1
The purpose of this paper is to expose and investigate natural phase-space formulations of two longstanding problems in the restriction theory of the Fourier transform. These probl…
Mizohata-Takeuchi inequalities for orthonormal systems
Jonathan Bennett, Neal Bez, Susana Gutierrez +2
We establish some weighted inequalities for Fourier extension operators in the setting of orthonormal systems. In the process we develop a direct approach to such inequalitie…
The oscillatory biest operator
Cristina Benea, Itamar Oliveira
We prove the boundedness of a trilinear operator that is modulation invariant and which contains curvature information given by the presence of a complex exponential, adding to the…
Probabilistic well-posedness of generalized cubic nonlinear Schrödinger equations with strong dispersion using higher order expansions
Jean-baptiste Casteras, Juraj Földes, Itamar Oliveira +1
In this paper, we study the local well-posedness of the cubic Schrödinger equation $$(i\partial_t + \mathcal{L}) u = \pm |u|^2 u \qquad \textrm{on} \quad \ I\times \mathbb{R}^d ,$…