Spectral permanence in a space with two norms

초록

A generalization of a classical argument of Mark G. Krein leads us to the conclusion that the Neumann Poincare operator associated to the Lame 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 Neinnann Poincare operator associated to the Laplace equation was stated by Poincare and aaa 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 Poincare operator, including also a discussion of spectral aavmptotica of a Galerkin type approximation. Several examples from function theory of a complex variable and harmonic analysis are included.

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