TITLE:
Reduced Vector Helmholtz Wave Equation Analysis on the Wave-Number Side
AUTHORS:
Randy Ott
KEYWORDS:
Helmholtz em Vector Wave Equation, Closed form of Resolvent, Sobolev Estimates for Solution
JOURNAL NAME:
Journal of Electromagnetic Analysis and Applications,
Vol.11 No.9,
September
29,
2019
ABSTRACT: 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.