Spectral properties of the Neumann-Poincar\'e operator on rotationally symmetric domains in two dimensions

Autor:	Ji, Yong-Gwan, Kang, Hyeonbae
Rok vydání:	2022
Předmět:	Mathematics - Spectral Theory 31A10 (primary) 35P05 30B10 (secondary)
Druh dokumentu:	Working Paper
Popis:	This paper concerns the spectral properties of the Neumann-Poincar\'e operator on $m$-fold rotationally symmetric planar domains. An $m$-fold rotationally symmetric simply connected domain $D$ is realized as the $m$th-root transform of a certain domain, say $\Omega$. We prove that the domain of definition of the Neumann-Poincar\'e operator on $D$ is decomposed into invariant subspaces and the spectrum on one of them is the exact copy of the spectrum on $\Omega$. It implies in particular that the spectrum on the transformed domain $D$ contains the spectrum on the original domain $\Omega$ counting multiplicities. Comment: 14 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2201.08077 Zobrazit plný text záznamu View this record from Arxiv