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Spectrum of the volume integral operator of the three-dimensional electromagnetic scattering is analyzed. The operator has both continuous essential spectrum, which dominates at lower frequencies, and discrete eigenvalues, which spread out at higher ones. The explicit expression of the operator's symbol provides exact outline of the essential spectrum for… (More)

We show that the mode corresponding to the point of essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root of the three-dimensional Dirac's delta function. An explicit expression for this singular mode in terms of the Weyl sequence is provided and analyzed. An essential resonance thus leads… (More)

- Yasuhide Fukumoto, Alexander B. Samokhin, MI
- 2011

We construct the singular mode corresponding to a spatial essential spectrum of the integral operator for the scattering of the electromagnetic waves by a three-dimensional body of finite size with inhomogeneous and anisotropic dielectric per-mittivity tensor. The permittivity tensor field is assumed to be Hölder continuous throughout the whole space. The… (More)

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