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 On dB spaces with nondensely defined multiplication operator and the existence of zero-free functions


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In this work we consider de Branges spaces where the multiplication operator by the independent variable is not densely defined. First, we study the canonical selfadjoint extensions of the multiplication operator as a family of rank-one perturbations. Then, on the basis of the obtained results, we provide new necessary and sufficient conditions for a real, zero-free function to lie in a de Branges space.



Author: Luis O. Silva; Julio H. Toloza

Source: https://archive.org/







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