Mémoires sur les fonctions complémentaires" / note in Comptes Rendus de l'Académie des Sciences, Paris, 19 (1844)¶
(1844). Mémoires sur les fonctions complémentaires" / note in Comptes Rendus de l'Académie des Sciences, Paris, 19 (1844).
Cited by¶
1 citation across 1 artifact.
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Primes¶
- Boundedness
- … with the requirement of bounded magnitude across all of $\mathbb{C}$ forces the function to be a constant, and the theorem has wide downstream consequences (the fundamental theorem of algebra; the maximum-modulus principle; the Schwarz lemma; the entire complex-dynamics theory of bounded holomorphic functions).
This sourcecombination of holomorphy with global boundedness forces constancy. [CITATION-FIX: the previously cited Liouville (1844) Comptes Rendus 18, 883–885 is Liouville's transcendental-numbers paper ('Sur des classes très-étendues de quantités...'), not the bounded-entire-function theorem — a conflation of two unrelated 1844 items.]
- … with the requirement of bounded magnitude across all of $\mathbb{C}$ forces the function to be a constant, and the theorem has wide downstream consequences (the fundamental theorem of algebra; the maximum-modulus principle; the Schwarz lemma; the entire complex-dynamics theory of bounded holomorphic functions).
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