Inverse problems aimed at locating cracks and voids inside a dielectric medium by means of electromagnetic waves involve knowledge of transmission eigenvalues. The subject has been actively investigated by many Authors for some years and results have been presented in articles and books. Unfortunately, the frequency dependence of dielectric permittivity and magnetic permeability of the material has not been taken into account. A theorem which provides existence and asymptotic properties of real transmission eigenvalues is shown to be physically inconsistent, because it ignores the Kramers - Kronig relations.
Crosta, G. (2015). Inverse spectral theory and KRAMERS-KRONIG relations. In C.J. Reddy, K. ElMahgoub (a cura di), 31st International Review of Progress in Applied Computational Electromagnetics, ACES 2015 (Williamsburg LodgeWilliamsburg; United States; 22-26 March 2015) (pp. 142-143). Golden, CO : Applied Computational Electromagnetics Society (ACES).
Inverse spectral theory and KRAMERS-KRONIG relations
CROSTA, GIOVANNI FRANCO FILIPPO
Primo
2015
Abstract
Inverse problems aimed at locating cracks and voids inside a dielectric medium by means of electromagnetic waves involve knowledge of transmission eigenvalues. The subject has been actively investigated by many Authors for some years and results have been presented in articles and books. Unfortunately, the frequency dependence of dielectric permittivity and magnetic permeability of the material has not been taken into account. A theorem which provides existence and asymptotic properties of real transmission eigenvalues is shown to be physically inconsistent, because it ignores the Kramers - Kronig relations.
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