# $L^p$-bounds on spectral clusters associated to polygonal domains

@article{Blair2015LpboundsOS,
title={\$L^p\$-bounds on spectral clusters associated to polygonal domains},
author={Matthew D. Blair and G. Austin Ford and Jeremy Louis Marzuola},
journal={Revista Matem{\'a}tica Iberoamericana},
year={2015}
}
• Published 1 April 2015
• Mathematics
• Revista Matemática Iberoamericana
We look at the $L^p$ bounds on eigenfunctions for polygonal domains (or more generally Euclidean surfaces with conic singularities) by analysis of the wave operator on the flat Euclidean cone $C(\mathbb{S}^1_\rho) := \mathbb{R}_+ \times \left(\mathbb{R} \big/ 2\pi\rho \mathbb{Z}\right)$ of radius $\rho > 0$ equipped with the metric $h(r,\theta) = d r^2 + r^2 \, d\theta^2$. Using explicit oscillatory integrals and relying on the fundamental solution to the wave equation in geometric regions…
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