  In this paper, we address non-radiating and cloaking problems exploiting the
surface equivalence principle, by imposing at any arbitrary boundary the
control of the admittance discontinuity between the overall object (with or
without cloak) and the background. After a rigorous demonstration, we apply
this model to a non-radiating problem, appealing for anapole modes and
metamolecules modeling, and to a cloaking problem, appealing for non-Foster
metasurface design. A straightforward analytical condition is obtained for
controlling the scattering of a dielectric object over a surface boundary of
interest. Previous quasi-static results are confirmed and a general closed-form
solution beyond the subwavelength regime is provided. In addition, this
formulation can be extended to other wave phenomena once the proper admittance
function is defined (thermal, acoustics, elastomechanics, etc.).
