Overcompleteness of Sequences of Reproducing Kernels in Model Spaces

Abstract.

We give necessary conditions and sufficient conditions for sequences of reproducing kernels (k_Θ(·, λ _n ))_n ≥ 1 to be overcomplete in a given model space K ^p_Θ where Θ is an inner function in H^∞,  p ∈ (1, ∞), and where (λ _n )_n ≥ 1 is an infinite sequence of pairwise distinct points of $\mathbb{D}.$ Under certain conditions on Θ we obtain an exact characterization of overcompleteness. As a consequence we are able to describe the overcomplete exponential systems in L² (0, a).