1. Singularities of the resolvent at the thresholds of a stratified operator: a general method
- Author
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Côme Goudjo, Bio Soumarou Chabi Gado, and Marc Durand
- Subjects
Semi-elliptic operator ,Operator (computer programming) ,Multiplication operator ,General Mathematics ,Mathematical analysis ,Spectrum (functional analysis) ,General Engineering ,Finite-rank operator ,Compact operator ,Eigenvalues and eigenvectors ,Quasinormal operator ,Mathematics - Abstract
Our problem is about propagation of waves in stratified strips. The operators are quite general, a typical example being a coupled elasto-acoustic operator H defined in ℝ2 × I where I is a bounded interval of ℝ with coefficients depending only on z∈I. One applies the ‘conjugate operator method’ to an operator obtained by a spectral decomposition of the partial Fourier transform Ĥ of H. Around each value of the spectrum (except the eigenvalues) including the thresholds, a conjugate operator may be constructed which ensures the ‘good properties’ of regularity for H. A limiting absorption principle is then obtained for a large class of operators at every point of the spectrum (except eigenvalues). If the point is a threshold, the limiting absorption principle is valid in a closed subspace of the usual one (namely L, with s>½) and we are interested by the behaviour of R(z), z close to a threshold, applying in the usual space L, with s>½ when z tends to the threshold. Copyright © 2004 John Wiley & Sons, Ltd.
- Published
- 2004
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