P. Grabner

activity

20212025

collaborators

4 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…

math.CA2024

Hyperuniform point sets on projective spaces

Johann S. Brauchart, Peter J. Grabner

We extend the notion of hyperuniformity to the projective spaces $RP^{d - 1}$ , $CP^{d - 1}$ , $HP^{d - 1}$ , and $OP^{2}$ . We show that hyperuniformity im…

math.CA2021

Weighted $L^{2}$ -Norms of Gegenbauer polynomials

Johann S. Brauchart, Peter J. Grabner

We study integrals of the form \begin{equation*} \int_{-1}^1(C_n^{(λ)}(x))^2(1-x)^α(1+x)^β\, dx, \end{equation*} where $C_{n}^{(λ)}$ denotes the Gegenbauer-polynomial of index $λ > 0$ …

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

Positive definite singular kernels on two-point homogeneous spaces

Hyperuniform point sets on projective spaces

Weighted L2-Norms of Gegenbauer polynomials

Weighted $L^{2}$ -Norms of Gegenbauer polynomials