We give a new characterization of character-automorphic Hardy spaces of order 2 and of their contractive multipliers in terms of de Branges Rovnyak spaces. Keys tools in our arguments are analytic extension and a factorization result for matrix-valued analytic functions due to Leech.
D. Alpay and M. Mboup. A characterization of Schur multipliers between character-automorphic Hardy spaces. Integral Equations and Operator Theory, vol. 62 (2008), pp. 455-463.