Nevanlinna–Pick interpolation

In complex analysis, given initial data consisting of ${\displaystyle n}$ points ${\displaystyle \lambda _{1},\ldots ,\lambda _{n}}$ in the complex unit disc ${\displaystyle \mathbb {D} }$ and target data consisting of ${\displaystyle n}$ points ${\displaystyle z_{1},\ldots ,z_{n}}$ in ${\displaystyle \mathbb {D} }$, the Nevanlinna–Pick interpolation problem is to find a holomorphic function ${\displaystyle \varphi }$ that interpolates the data, that is for all ${\displaystyle i}$,

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