4 papers · 1 filter
Fourier restriction estimates based on -dimensions: beyond Stein--Tomas
Marc Carnovale, Jonathan M. Fraser, Ana E. de Orellana
The well-known Stein--Tomas restriction theorem gives the sharp range of for which restriction estimates hold for the surface measure on the sphere. This was gener…
On the number of 3APs in fractal sets
Marc Carnovale, Steven Senger
We use techniques from the study of the Falconer distance conjecture to explore conditions which guarantee largeness (in terms of bounded density/Lebesgue measure and Hausdor…
restriction estimates from the Fourier spectrum
Marc Carnovale, Jonathan M. Fraser, Ana E. de Orellana
The Stein--Tomas restriction theorem is an important result in Fourier restriction theory. It gives a range of for which restriction estimates hold for a given mea…
Obtaining the Fourier spectrum via Fourier coefficients
Marc Carnovale, Jonathan M. Fraser, Ana E. de Orellana
The Fourier spectrum is a family of dimensions that interpolates between the Fourier and Hausdorff dimensions and are defined in terms of certain energies which capture Fourier dec…