Another look at the Burns-Krantz theorem |
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Authors: | David Shoikhet |
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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 |
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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 in term of relations among three boundary
derivatives of the function at this point. |
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Keywords: | |
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