Complétude des noyaux reproduisants dans les espaces modèles. (Completeness of reproducing kernels in the model spaces) (Q1613956)

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., \(k_\Theta(z,\lambda)= {1-\overline{\Theta(\lambda)}\Theta\over 1-\overline\lambda z}\).