Another look at the Burns-Krantz Theorem

David Shoikhet

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Another look at the Burns-Krantz Theorem

David Shoikhet

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Abstract

We obtain a generalization of the Burns-Krantz rigidity theorem for holomorphic self-mappings of the unit disk in the spirit of the classical Schwarz-Pick Lemma and its continuous version due to L.Harris via the generation theory for one-parameter semigroups. In particular, we establish geometric and analytic criteria for a holomorphic function on the disk with a boundary null point to be a generator of a semigroup of linear fractional transformations under some relations between three boundary derivatives of the function at this point.

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David Shoikhet. 2007-02-13. Another look at the Burns-Krantz Theorem. https://arxiv.org/abs/math/0702377

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