P. Grabner

collaborators

2 papers

math.CA2025

Leading order asymptotics for non-local energies and the Read-Shockley law

Peter J. Grabner, Florian Theil

We study an energy minimization problem $\sum_{i \neq = j} W (z_{i} - z_{j})$ for $N$ points ${z_{1}, \dots, z_{N}}$ with applications in dislocation theory. The $N$ points lie i…

math.CA2024

Positive definite singular kernels on two-point homogeneous spaces

Dmitriy Bilyk, Peter Grabner

We study positive definiteness of kernels $K (x, y)$ on two-point homogeneous spaces. As opposed to the classical case, which has been developed and studied in the existing literatur…