| Abstract: | The backward shift operator $L$ acts on analytic functions defined in the unit disk by the formula $L : f(z) \mapsto \frac{f(z)-f(0)}{z}$. Its importance comes from the twin operator theories of Nagy-Foias and de Branges-Rovnyak, which assert that, under minor technical assumptions, every contractive linear operator on a Hilbert space is equivalent to $L$ on a suitable Hilbert space of analytic functions. In this talk we will study explore the structure of analytic function spaces under the assumption of contractive backward shift. In particular, we will talk about a class of spaces generalizing the classical de Branges-Rovnyak spaces and say something about problems of polynomial and continuous approximation in these spaces. |
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