Abstract. A new theory of regular functions over the skew field of Hamilton numbers (quaternions) and in the division algebra of Cayley numbers (octonions) has been recently introduced by Gentili and Struppa (Adv. Math. 216 (2007) 279–301). For these functions, among several basic results, the analogue of the classical Schwarz’ Lemma has been already obtained. In this paper, following an interesting approach adopted by Burns and Krantz in the holomorphic setting, we prove some boundary versions of the Schwarz’ Lemma and Cartan’s Uniqueness Theorem for regular functions. We are also able to extend to the case of regular functions most of the related “rigidity” results known for holomorphic functions.

Rigidity for regular functions over Hamilton and Cayley numbers and a boundary Schwarz lemma / G. GENTILI; F. VLACCI. - In: INDAGATIONES MATHEMATICAE. - ISSN 0019-3577. - STAMPA. - 19 (4):(2008), pp. 535-545. [10.1016/S0019-3577(09)00011-1]

Rigidity for regular functions over Hamilton and Cayley numbers and a boundary Schwarz lemma

GENTILI, GRAZIANO;VLACCI, FABIO
2008

Abstract

Abstract. A new theory of regular functions over the skew field of Hamilton numbers (quaternions) and in the division algebra of Cayley numbers (octonions) has been recently introduced by Gentili and Struppa (Adv. Math. 216 (2007) 279–301). For these functions, among several basic results, the analogue of the classical Schwarz’ Lemma has been already obtained. In this paper, following an interesting approach adopted by Burns and Krantz in the holomorphic setting, we prove some boundary versions of the Schwarz’ Lemma and Cartan’s Uniqueness Theorem for regular functions. We are also able to extend to the case of regular functions most of the related “rigidity” results known for holomorphic functions.
2008
19 (4)
535
545
G. GENTILI; F. VLACCI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/261811
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