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A Schur transformation for functions in a general class of domains. (English) Zbl 1254.30029

Summary: In this paper we present a framework in which the Schur transformation and the basic interpolation problem for generalized Schur functions, generalized Nevanlinna functions and the like can be studied in a unified way. The basic object is a general class of functions for which a certain kernel has a finite number of negative squares. The results are based on and generalize those in previous papers of the first three authors on the Schur transformation in an indefinite setting.

MSC:

30E05 Moment problems and interpolation problems in the complex plane
47A57 Linear operator methods in interpolation, moment and extension problems
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