## 1 Introduction
In [34], we developed the general theory in abstract form to model angular regions filled by arbitrary linear media and we reported its implementation only for isotropic media. In the present work, we propose a complete theoretical package for solving diffraction problems with impenetrable wedges immersed in an arbitrary linear medium; in addition, this package is extendable to multiple penetrable angular regions. The proposed method exploits the combination and the extension of powerful mathematical tools developed in different contexts. The first tool is the Bresler-Marcuvitz (BM) transverse equation theory for layered media [33; 35], the second is the characteristic Green function procedure [36; 37], the third one is the Wiener-Hopf technique [33; 38] in its generalized form [11; 12], and the fourth one (which is a completely novel contribution) is the direct application of Fredholm factorization to generalized Wiener-Hopf equations (GWHEs). The method starts with an extension of transverse equation theory for layered arbitrary linear media applied to the stratification of an angular shaped region with the help of abstract BM notation. We then apply the characteristic Green function procedure to obtain the solution of equations in angular geometries. The solutions defined at the faces of the angular region are spectral functional equations that relate continuous (tangential) field components of the two faces delimiting a homogeneous angular region. The application of boundary conditions yields a system of generalized Wiener-Hopf equations (GWHEs), where _generalized_ means that the field components of each face are defined into different complex planes but related to one another. The GWHEs preserve the characteristic form of classical Wiener-Hopf equations (CWHEs), where the system of equations presents a kernel and plus and minus unknowns; however, the plus and minus unknowns are defined into different complex planes which are related to one another. The functional equationsand GWHEs of angular regions can be suitably interpreted with a network formalism, as is common for classical layered regions using transmission line theory. This circuit/network modeling representation of angular regions allows for the description of the technique with systematic steps to avoid redundancy. This capability is particularly useful when dealing with complex scattering problems, where we break down the complexity of a geometry into subdomains of canonical shape. These subdomains are modeled via spectral functional equations or related integral representations that can be interpreted through a network approach (obtained once and for all) and are capable of modeling the entire complex problem through the composition of circuital relationships; see, for instance, [30; 31; 32]. In the presence of an isotropic medium (and further special cases of more general media), a suitable mapping reduces the GWHEs to CWHEs, which in certain cases are amenable of exact solutions; alternatively, we can resort to the semi-analytical/approximate general-purpose factorization method, that is, Fredholm factorization, which reduces the factorization problem to Fredholm Integral Equations (FIEs) of the second kind. This technique was presented in the early 2000s for CWHEs; it was first effectively applied in impenetrable and penetrable wedge problems immersed in isotropic media [11; 12], and more recently in isotropic complex scattering problems [30; 31; 32]. The main constraint in the present work resides in the complexity of media that do not allow mappings between complex planes of GWHEs for their transformation into CWHEs. Consequently, when dealing with arbitrary linear media in particular, we propose relying on a novel version of the versatile approximate method known as Fredholm factorization. Here, for the first time, we apply the Fredholm factorization method directly to GWHEs as a regularization tool.