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Complétude des noyaux reproduisants dans les espaces modèles. (Completeness of reproducing kernels in the model spaces). (French) Zbl 1032.46040
For \(1< p<\infty\), the model space \(K^p_\theta\) is defined by \(K^p_\Theta= H^p\cap\Theta\overline{H^p_0}\), where \(\Theta\) is an inner function.
The author studies the problem of when the system \(k_\Theta(\cdot,\lambda_n)\), \(|\lambda_n|< 1\), is complete in \(K^p_\Theta\), where \(k_\Theta(\cdot,\lambda)\) is the reproducing kernel of \(K^p_\Theta\), i.e., \(k_\Theta(z,\lambda)= {1-\overline{\Theta(\lambda)}\Theta\over 1-\overline\lambda z}\).

MSC:
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
30C40 Kernel functions in one complex variable and applications
30D55 \(H^p\)-classes (MSC2000)
47A15 Invariant subspaces of linear operators
47B32 Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
47B38 Linear operators on function spaces (general)
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