Spectral Resolution of the Neumann-Poincar, 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, 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 of the plasmon resonance at the absolutely continuous spectrum.