Spectral permanence in a space with two norms

  • Hyeonbae Kang

    Inha University, Incheon, Republic of Korea
  • Mihai Putinar

    University of California, Santa Barbara, USA and Newcastle University, UK
Spectral permanence in a space with two norms cover
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A generalization of a classical argument of Mark G. Krein leads us to the conclusion that the Neumann–Poincar´e operator associated to the Lamé system of linear elastostatics equations in two dimensions has the same spectrum on the Lebesgue space of the boundary as the more natural energy space. A similar result for the Neumann–Poincaré operator associated to the Laplace equation was stated by Poincaré and was proved rigorously a century ago by means of a symmetrization principle for non-selfadjoint operators. We develop the necessary theoretical framework underlying the spectral analysis of the Neumann–Poincaré operator, including also a discussion of spectral asymptotics of a Galerkin type approximation. Several examples from function theory of a complex variable and harmonic analysis are included.

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Hyeonbae Kang, Mihai Putinar, Spectral permanence in a space with two norms. Rev. Mat. Iberoam. 34 (2018), no. 2, pp. 621–635

DOI 10.4171/RMI/998