Premium
The dyadic Green's function as an inverse operator
Author(s) -
Collin R. E.
Publication year - 1986
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs021i006p00883
Subject(s) - eigenfunction , mathematics , operator (biology) , scalar (mathematics) , mathematical analysis , inverse , function (biology) , function representation , point (geometry) , green's function for the three variable laplace equation , scalar field , laplace's equation , physics , partial differential equation , eigenvalues and eigenvectors , geometry , mathematical physics , quantum mechanics , combinatorics , repressor , evolutionary biology , biology , transcription factor , boolean function , biochemistry , chemistry , gene
It is shown that the integral of the scalar product of the current density with the electric field dyadic Green's function can be carried out without difficulty by allowing the observation point to be an arbitrarily located point within a small spherical volume and using an appropriate representation for the Green's dyadic function obtained from the eigenfunction expansion. On the basis of this result it is established that the integral operator using the Green's dyadic function is the correct inverse operator for the vector wave equation provided the integration is taken over the whole volume (the support of the current density).