Transmutation Operator for the Radial Maxwell System in Inhomogeneous Media

In this paper, we revisit Kravchenko’s method for analyzing the radial static Maxwell system in a three-dimensional inhomogeneous isotropic medium:

$$\begin{aligned} \left\{ \begin{array}{ll} \operatorname {div}(\varepsilon \overrightarrow{E}) & = 0, \\ \operatorname {curl} \overrightarrow{E} & = 0, \end{array} \right. \end{aligned}$$

where the coefficient function \(\varepsilon \) is assumed to be a radial analytic function. By introducing a new class of modified normalized systems of functions with respect to the Dirac operator, we construct a transmutation operator that maps vector-valued monogenic functions into solutions of the system.