## 1 Introduction  
The great interest in studying electromagnetic scattering from thin objects originates from the huge number of applications in which they are involved: frequency selective surfaces, antennas, radomes, tree leaves models, etc. More recently, the discovery of graphene [1], which is a planar monolayer of carbon atoms with amazing electronic, optical, thermal, and mechanical properties, and the consequent countless number of devices imagined to be made with such a material, have been leading to an impressive push towards the accurate study of lossy thin structures. Boundary and radiation conditions together with the local power boundedness condition allow to formulate a uniquely solvable boundary value problem for the Maxwell equations, for which, in general, no closed form solutions are available, except for problems involving suitable canonical structures [2]. In other cases, only approximate solutions are provided based on Rayleigh-Gans or physical optics [3; 4; 5]. Consequently, the analysis of general structures or the search for more accurate solutions require the use of numerical methods. Amongst them, the classical Moments' method approach is generally preferred because the unknowns and the integral equations are defined on finite supports, the radiation condition is automatically satisfied by the proper selection of the Green's function of the problem and the local power boundedness condition is guaranteed by the correct definition of the functional space at which the unknowns belong. Unfortunately, the discretization of a 3-D problem is generally onerous in terms of storage requirements. On the other hand, when the thickness is much smaller than the wavelength, the scatterer can be modelled as an infinitesimally thin structure described in terms of suitable generalized boundary conditions [6]. Just for an example, this is what happens when dealing with a graphene object, for which the surface impedance can be obtained from the graphene surface conductivity provided by the Kubo formalism [7]. According to this approach, the boundary value problem for the Maxwell equations at hand can be equivalently formulated in terms of a uniquely solvable system of 2-D singular integral equations for the effective surface current densities [8; 9]. It is worth noting that, due to the singular nature of the obtained integral equations, nothing can be established a priori about the existence of the solution. Moreover, the convergence of the approximate solution, obtained by adopting a discretization scheme, to the exact one, if it exists, cannot be, in general, predicted [10]. Anyway, ill-conditioned and/or dense matrices can result from a direct discretization. One way to overcome all these problems is represented by the methods of analytical regularization [11]. Such methods are aimed at individuating a suitable singular part of the integral operator, containing the most singular part of the operator itself, to be analytically inverted. The selection of such an operator depends on the problem at hand. Usually, it can be a suitable asymptotic part (e.g., the static part or the high-frequency part, etc.) or a canonical-shape part, which can be inverted by means of functional techniques such as Wiener-Hopf, Cauchy, Titchmarsh, Abel, Riemann-Hilbert Problem, and the separation of variables techniques [12; 13; 14; 15; 16; 17; 18; 19; 20]. Following this line of reasoning, the resulting integral equation is of the Fredholm second-kind; hence, the Fredholm theory [21], generalized by [PERSON] for operators [22], can be applied. As a result, the existence originates from the uniqueness and the convergence of a discretization scheme preserving the Fredholm second-kind nature of the obtained integral equation is guaranteed. On the other hand, a proper choice of the discretization scheme can lead directly to a Fredholm second-kind matrix equation.