The resolvent helps solve a PDE defined on all of wave-number space, . Almost all electromagnetic scattering problems have been solved on the spatial side and use the spatial Green’s function approach. This work is motivated by solving an EM problem on the Fourier side in order to relate the resolvent and the Green’s function. Methods used include Matrix Theory, Fourier Transforms, and Green’s function. A closed form of the resolvent is derived for the electromagnetic Helmholtz reduced vector wave equation, with Dirichlet boundary conditions. The resolvent is then used to derive expressions for the solution of the EM wave equation and provide Sobolev estimates for the solution.
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机译：Gaikin Shitsu Vector Kukan No Zeta Kansu No Kansu Utoushikini Arawareru MATRIX No DETERMINANT NITITE REDUCE3.2 Noriyo Kaikinshitu Vector Kuukan No Saikin No Hatten
