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| Volume 8, Number 1, April 2007, pp. 99-103 | |||||||||
| Marina Levenshtein, Simeon Reich, and David Shoikhet | |||||||||
| Key words: | |||||||||
| Angular derivative, boundary fixed point, continuous one-parameter semigroup, Denjoy-Wolff point, holomorphic generator, resolvent. | |||||||||
| Mathematices Subject Classification: Primary 30C45, 30D05, 47H20. | |||||||||
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| Abstract: | |||
| Let f be the generator of a one-parameter continuous semigroup of holomorphic self-mappings of the open unit disk ∆ in the complex plane. We use the resolvent method to show that if for some boundary point τ of ∆, the angular limit ∠ lim z → τ f (z )/|z - τ|3 = 0, then f vanishes identically in ∆. | |||
| An application of the resolvent method to rigidity theory for holomorphic mappings | ||