Another look at the Burns-Krantz theorem
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- Shoikhet, D. J Anal Math (2008) 105: 19. doi:10.1007/s11854-008-0030-8
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.