Nevanlinna–Pick interpolation

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

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