Generalized Modes in an Acoustic Strip

Croc, Elisabeth; Dermenjian, Yves

doi:10.1007/978-1-4612-1878-4_6

Cited by 2 publications

(1 citation statement)

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“…A point ∈ (H ) is said to be a threshold if there exist n and such that n ( ) = and n ( ) = 0. When H is acoustic, elastic or electromagnetic, the results about its spectral theory are already known [1,[4][5][6]. They were obtained by studying the dispersion curves and by constructing their resolvents or via the Mourre's method for the acoustic case [7,8].…”

Section: Hamiltonians In a Stratified Stripmentioning

confidence: 99%

Singularities of the resolvent at the thresholds of a stratified operator: a general method

Gado¹,

Durand²,

Goudjo³

2004

Math Methods in App Sciences

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SUMMARYOur problem is about propagation of waves in stratiÿed strips. The operators are quite general, a typical example being a coupled elasto-acoustic operator H deÿned in R 2 × I where I is a bounded interval of R with coe cients depending only on z ∈ I . One applies the 'conjugate operator method' to an operator obtained by a spectral decomposition of the partial Fourier transformĤ 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 2 s , with s¿ 1 2 ) and we are interested by the behaviour of R(z), z close to a threshold, applying in the usual space L 2 s , with s¿ 1 2 when z tends to the threshold.

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Section: Hamiltonians In a Stratified Stripmentioning

confidence: 99%