Inverse spectral Love problem via Weyl-Titchmarsh function

Abstract

In this paper we prove an inverse resonance theorem for the half-solid with vanishing stresses on the surface via Weyl-Titchmarsh function. Using a semi-classical approach it is possible to simplify this three-dimensional problem of the elastic wave equation for the half-solid as a Schrödinger equation with Robin boundary conditions on the half-line. The goal of the paper is to establish a method to recover the potential from the Weyl-Titchmarsh function for non self-adjoint problems and to establish a one-to-one and onto map between suitable function spaces. Moreover, we produce an algorithm in order to retrieve the shear modulus from the eigenvalues and resonances, via the spectral data.

arXiv comment26 pages, 1 figure

References in corpus (8)

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• Periodic Jacobi operator with finitely supported perturbation on the half-lattice
• Semiclassical analysis of elastic surface waves
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• Inverse Regge poles problem on a warped ball
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