Abstract
By Cayley transformation, there is an interplay between matrix-valued Caratheodory and Schur functions in the unit disk. One of the main aims of the paper is to study this interplay with a view to the fact that the matrix function given by the values of a Caratheodory function via Moore–Penrose inverses is also a Caratheodory function. In doing so, we also analyze ranges and null spaces of the values of the matrix function in question and get some results of independence concerning the concretely chosen point of the domain.
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