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Another look at the Burns-Krantz theorem
Authors:David Shoikhet
Institution:(1) Department of Mathematics, ORT Braude College, P.O. Box 78, 21982 Karmiel, Israel;(2) Department of Mathematics, The Technion — Israel Institute of Technology, 32000 Haifa, Israel
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 in term of relations among three boundary derivatives of the function at this point.
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