Spectral permanence in a space with two norms

• Hyeonbae Kang ^[1] ; Mihai Putinar ^[2]
  1. [1] Inha University

     Inha University

     Corea del Sur

     
  2. [2] University of California
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 2, 2018, págs. 621-635
• Idioma: inglés
• DOI: 10.4171/RMI/998
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.