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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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