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 i...
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| Veröffentlicht in: | Integral equations and operator theory 2006-09, Vol.56 (1), p.45-56 |
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| container_title | Integral equations and operator theory |
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| creator | Chalendar, I. Fricain, E. Partington, J. R. |
| description | 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 $L^2(0, a)$. |
| doi_str_mv | 10.1007/s00020-005-1413-1 |
| format | Article |
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| ispartof | Integral equations and operator theory, 2006-09, Vol.56 (1), p.45-56 |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Mathematics |
| title | Overcompleteness of Sequences of Reproducing Kernels in Model Spaces |
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