Abstract
This paper concerns the matrix condition necessary and sufficient for the existence of a function f, holomorphic in a finitely connected domain and having |f| ≤ 1 and finitely many first prescribed Taylor coefficients at a finite number of given points. In a simply connected domain, some transformation formulas and their applications are given. The results of Abrahamse on the Pick interpolation problem are generalized to the above extended interpolation problem.
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