Abstract
The Nevanlinna-Pick-Caratheodory-Fejer interpolation problem with finitely many interpolation conditions is considered in the class Sκ of meromorphic functions f with κ poles inside the unit disk D and with ‖ f‖L∞(T) 1 . Necessary and sufficient conditions for the existence and for the uniqueness of a solution are given in terms of the Pick matrix P of the problem explicitly determined from interpolation data. In particular it is shown that the problem admits infinitely many solutions if and only if κ is not less than the number of nonpositive eigenvalues of P . For κ equal to the number of nonpositive eigenvalues of P , we describe the solution set of the problem. Also we present necessary and sufficient conditions for the existence of a meromorphic function with a given pole multiplicity satisfying interpolation conditions and having the minimal possible L∞ -norm on the unit circle T . Mathematics subject classification (2010): 30E05.
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