  We present the mathematical theory of one-dimensional infinitely periodic
chains of subwavelength resonators. We analyse both Hermitian and non-Hermitian
systems. Subwavelength resonances and associated modes can be accurately
predicted by a finite dimensional eigenvalue problem involving a capacitance
matrix. We are able to compute the Hermitian and non-Hermitian Zak phases,
showing that the former is quantised and the latter is not. Furthermore, we
show the existence of localised edge modes arising from defects in the
periodicity in both the Hermitian and non-Hermitian cases. In the non-Hermitian
case, we provide a complete characterisation of the edge modes.
