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Wave splitting of Maxwell's equations with anisotropic heterogeneous constitutive relations
1.  Electromagnetic Engineering, School of Electrical Engineering, Royal Institute of Technology, SE100 44 Stockholm, Sweden 
In the process of defining the wavefield decomposition (wavesplitting), the resolvent set of the timeLaplace representation of the system's matrix is analyzed. This set is shown to contain a strip around the imaginary axis. We construct a splitting matrix as a DunfordTaylor type integral over the resolvent of the unbounded operator defined by the electromagnetic system's matrix. The splitting matrix commutes with the system's matrix and the decomposition is obtained via a generalized eigenvalueeigenvector procedure. The decomposition is expressed in terms of components of the splitting matrix. The constructive solution to the question of the existence of a decomposition also generates an impedance mapping solution to an algebraic Riccati operator equation. This solution is the electromagnetic generalization in an anisotropic media of a DirichlettoNeumann map.
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