Joel Nathe

collaborators

4 papers

math.AP2026

Recovery of a Null Form in the Wave Equation from Scattering Data

Joel Nathe

We use highly oscillatory geometric optics solutions to solve the inverse problem for the system $$ \square \begin{bmatrix} u^{(1)}\\ u^{(2)}\\ \vdots\\ u^{(n)}\end{bmatrix} = \sum…

math.AP2026

The Recovery of Semilinear Potentials Satisfying Null Conditions From Scattering Data

Joel Nathe, Antônio Sá Barreto

We construct oscillatory solutions of fully semilinear wave equations in Minkowski space satisfying a null condition of the form $$\square u:=(-\partial_{x_0}^2 +\sum_{j=1}^n \part…

math.CA2024

Subharmonic Kernels and Energy Minimizing Measures, with Applications to the Flat Torus

Steven B. Damelin, Joel Nathe

We study the minimization of the energy integral $I_{K} (μ) = \int_{Ω} \int_{Ω} K (x, y) d μ (x) d μ (y)$ over all Borel probability measures $μ$ , where $(Ω, ρ)$ is a compact connected metric sp…

math.CA2024

Geodesic Distance Riesz Energy on Projective Spaces

Dmitriy Bilyk, Ryan W. Matzke, Joel Nathe

We study probability measures that minimize the Riesz energy with respect to the geodesic distance $ϑ (x, y)$ on projective spaces $FP^{d}$ (such energies arise from…