Inverse spectral theory and KRAMERS-KRONIG relations

Author

Crosta, Giovanni Franco

Author_Institution

Dept. of Earth- & Environ. Sci., Univ. of Milan Bicocca, Milan, Italy

fYear

2015

fDate

22-26 March 2015

Firstpage

1

Lastpage

2

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.

Keywords

Kramers-Kronig relations; cracks; eigenvalues and eigenfunctions; inverse problems; magnetic permeability; permittivity; voids (solid); Kramers-Kronig relations; asymptotic properties; cracks; dielectric medium; dielectric permittivity; electromagnetic waves; frequency dependence; inverse spectral theory; magnetic permeability; real transmission eigenvalues; transmission eigenvalues; voids; Dielectrics; Eigenvalues and eigenfunctions; Inverse problems; Media; Permeability; Permittivity; Refractive index; KRAMERS-KRONIG relations; Transmission eigenvalues; dielectric permittivity; high frequency asymptotics;

fLanguage

English

Publisher

ieee

Conference_Titel

Applied Computational Electromagnetics (ACES), 2015 31st International Review of Progress in

Conference_Location

Williamsburg, VA

Type

conf

Filename

7109654