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A note on pairwise distances preserving and Nevanlinna-Pick interpolation theorem

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In this note, we prove that if pairwise distances are preserved for $n$-points in the unit disc, then there exists a holomorphic or anti-holomorphic interpolation function from the unit disc to itself.

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In this note, we prove that if pairwise distances are preserved for $n$-points in the unit disc, then there exists a holomorphic or anti-holomorphic interpolation function from the unit disc to itself.

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