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Given the reproducing kernel k of the Hilbert space Hk we study spaces Hk(b) whose reproducing kernel has the form k(1−bb⁎), where b is a row-contraction on Hk. In terms of reproducing kernels this is the most far-reaching generalization of the classical de Branges-Rovnyaks spaces, as well as their very recent generalization to several variables. This includes the so called sub-Bergman spaces [31]
