TABLE OF CONTENTS Electromagnetic field problems may be expressed in operator form as
| (2.150) |  |
where L is a linear operator, g is the known field and f the unknown field or source. As an example we may establish an equation of the type Z( J) = E with Z an impedance operator, J the unknown current and E the known electric field; or we may deal with an equation of the type Y( E) = H where Y is an admittance operator, E is the unknown electric field and H is the known magnetic field. Detailed expressions of the above ammittance operators are found, for instance, in Chapter 5 when dealing with step discontinuities in planar dielectric waveguides.
In general, we may be interested in the field f itself, or in finding a functional ? of the type
| (2.151) |  |
which may express immittances, scattering parameters or other quantities of interest. In (2.151) the function h is suitably selected and is a known continuous function, so that ? is a continuous linear functional. The inner product appearing in (2.151) is a reaction as defined by (2.129). In addition to (2.150) it is also appropriate to consider the adjoint operator L and the adjoint equation
| (2.152) |  |
By using (2.152), (2.150) and the definition of adjoint, the following equivalences are obtained
| (2.153) |  |
which may be viewed as a reciprocity theorem of...
