Overcompleteness of Sequences of Reproducing Kernels in Model Spaces |
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Authors: | I Chalendar E Fricain J R Partington |
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Institution: | (1) Institut Girard Desargues, UFR de Mathématiques, Université Claude Bernard Lyon 1, F-69622 Villeurbanne Cedex, France;(2) School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom |
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Abstract: | We give necessary conditions and sufficient conditions for sequences of reproducing kernels (kΘ(·, λn))n ≥ 1 to be overcomplete in a given model space KΘp where Θ is an inner function in H∞, p ∈ (1, ∞), and where (λn)n ≥ 1 is an infinite sequence of pairwise distinct points of
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). |
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Keywords: | Primary 46E22 46B15 |
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