Journal d'Analyse Mathématique

, Volume 105, Issue 1, pp 19–42

Another look at the Burns-Krantz theorem


DOI: 10.1007/s11854-008-0030-8

Cite this article as:
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.

Copyright information

© Hebrew University Magnes Press 2008

Authors and Affiliations

  1. 1.Department of MathematicsORT Braude CollegeKarmielIsrael
  2. 2.Department of MathematicsThe Technion — Israel Institute of TechnologyHaifaIsrael

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