Spectral resolution of the Neumann-Poincar\'{e} operator on intersecting disks and analysis of plasmon resonance

Abstract

The purpose of this paper is to investigate the spectral nature of the Neumann-Poincar\'e operator on the intersecting disks, which is a domain with the Lipschitz boundary. The complete spectral resolution of the operator is derived, which shows in particular that it admits only the absolutely continuous spectrum, no singularly continuous spectrum and no pure point spectrum. We then quantitatively analyze using the spectral resolution the plasmon resonance at the absolutely continuous spectrum.