Corpus ID: 221557848

Infinitely many embedded eigenvalues for the Neumann-Poincar\'e operator in 3D

  title={Infinitely many embedded eigenvalues for the Neumann-Poincar\'e operator in 3D},
  author={Wei Li and Karl-Mikael Perfekt and Stephen P. Shipman},
  journal={arXiv: Functional Analysis},
This article constructs a surface whose Neumann-Poincare (NP) integral operator has infinitely many eigenvalues embedded in its essential spectrum. The surface is a sphere perturbed by smoothly attaching a conical singularity, which imparts essential spectrum. Rotational symmetry allows a decomposition of the operator into Fourier components. Eigenvalues of infinitely many Fourier components are constructed so that they lie within the essential spectrum of other Fourier components and thus… Expand
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