Overcompleteness of Sequences of Reproducing Kernels in Model Spaces

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 $H^\infty$, $p ∈ (1,∞)$, and where $(λ_n)_{n≥1}$ is an infinite sequence of pairwise distinct points in the open unit disc. 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 $L^2(0, a)$.