Necessary and sufficient conditions for extending a function to a Schur function

A criterion for a function given by its values (with multiplicities) at a sequence of points in the disc $\mathbb D=\{|z|<1\}$ to extend to a holomorphic function in $\mathbb D$ with modulus at most $1$ is stated and proved. In the case when the function is defined by the values of its derivatives at $z=0$, this coincides with Schur's well-known criterion.
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