BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Reproducing kernel spaces and the Bargmann-Schiffer lemma Alpay, Daniel


We give a survey of the theory of reproducing kernel spaces of the kind defined by de Branges and Rovnyak and how they can be used to study Nevanlinna functions. In particular we give a proof of the Bargmann-Schiffer lemma. The advantages of the approach are that one can consider the matrix-valued case and also the case of generalized Nevanlinna functions, i.e. when the underlying kernel has a finite number of negative squares. We will also present a unified setting, which contains in particular the case of Schur functions and Nevanlinna functions in a unified framework.

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